In the original Back to the Future entry, we see very clearly the complications of altering a timeline. As Marty McFly explores the world of 1955, he is confronted with the fact that the history he learned of the events of his parent's life is changing before his eyes, and his own existence is in jeopardy. He has interfered with the meeting of his parents, and must correct the situation before it's too late, or he will cease to exist. This is very valuable to us, because right from the beginning we can see two distinct timelines: the original A-B timeline in which George McFly gets hit by a car, marries the daughter of the man who hit him, and lives the rest of his life as something of a nerd and a loser; and the altered timeline, in which Marty has prevented that, and is trying to correct it. It appears at first glance that we have an N-Jump: an original timeline which ends at the point at which Marty returns to the past, and an altered timeline which continues into the future beyond his return to the future.
However, this is not the case; and neither this movie nor any of the sequels recognizes this. We have not an N-Jump, but either an infinity loop or a sawtooth snap (both illustrated at the beginning of our Temporal Anomalies site, along with the N-Jump). Let me explain this.
In our A-B timeline, shortly after point A, George McFly meets Lorraine (through the aforementioned accident), marries her, and gets a job working for the bully who has terrorized him all his life, Biff. They have three children, the third of which takes an interest in music, and so connects with Doc, who provides him with access to technological equipment he might not otherwise have had. As a guitarist myself, I am quite aware that amplifiers, effects boxes, mixers, microphones, and other equipment all cost a great deal of money. Being able to repair or even build some of these things for your own use is a bonus, and Doc has the skills to do so. Marty would find his friendship with Doc useful in this way, and Doc would enjoy having the lad around, teach him bits about the equipment, and use his help in some of his experiments. This is the relationship we see at the beginning of the movie. Eventually, at point B, just after Doc is shot (and probably killed), Marty ends this timeline completely by returning to 1955, creating point C.
Point C, as you will recall from our study of Terminator, is the exact same moment in history as point A, but is now different because Marty McFly is there; had he made no other changes in time, his presence alone would be enough to make this a different timeline. In this timeline, Marty prevents the initial meeting of his parents, and, aided by Doc, recognizes that his existence is threatened.
I will interrupt this retelling to make my minor complaints: the photograph and the vanishing talent are not reasonable. The Marty McFly who carries the photo comes from a divergent timeline in which those people all exist; he was born, he has his own life history and existence. These things will continue to exist as long as he does. Even if our divergent timeline approach is not the truth, a logical consideration of the matter will quickly dispense with any notion of these "symptoms" of the temporal anomaly being possible. Marty McFly is in theory vanishing because his parents have not gotten together in the future which is his past; but it is not yet determined whether they will or will not get together. The fact that he is attempting to restore the future history proves that they might still get married. His existence is not a percent of probability--he is not less real or more real based on the likelihood of his birth! Were that the case, he would become non corporeal, ghostly, and lose the ability to affect reality at all. At the moment he arrives in the past, he either is real or is not real, and he remains in that state until he either leaves the past or dies there. The picture either exists or it does not--the changing images are foolish. How could the theoretical other picture even exist? No version of Marty McFly would be carrying a picture of that place with no one in it; nor would the picture make any sense if he were standing on one end, alone in the picture. And a picture of Marty's brother without his head is far more absurd! No, this Marty has a picture, and the picture does not change. Nor does he: he is who he is. He may have no future, but he has a past in an alternate timeline.
However, I will excuse these minor gripes. They make good plot devices, communicating quickly to the viewer the serious nature of his situation. Marty McFly might cease to exist, and that is serious--not merely for McFly, but for all of time. If Marty McFly is never born, all of time is trapped in an infinity loop.
Follow this: let us suppose that Marty is unable to repair the damage he has done; let us further suppose that no one else intervenes to repair this damage. (It would be possible that somehow George and Lorraine would still meet and marry, perhaps after high school, under other circumstances, and Marty would still be born; as unlikely as it seems, it is important to remember that Marty does not have to be the one to fix the timeline, as long as the timeline is repaired.) Now George does not marry Lorraine, and Marty is not born. Since Marty is not born, he does not return in Doc's time machine; and therefore he does not interfere in the meeting of his parents, and therefore he is born, and therefore he does. These two alternate histories would repeat in perpetuity.
However, that is not what happened. Marty did arrange for his parents to get together (albeit not quite as he had planned), and the incidental result was that all of the future was changed. We get a look at that altered history at the end of the movie: George McFly is a successful sci-fi author (undoubtedly encouraged by his son years before), and the family is much more upscale. Biff is not George's boss, but an auto mechanic who is grateful for the opportunity to clean George's cars for a little extra cash. It is a fortunate point that no drastic changes occurred--the family did not buy a different house, but made this one nicer; they had the same three children, Jennifer was still his girlfriend, and he even was planning the same weekend in the mountains--but the changes are major, and Marty's life was very different.
And this is why it's not an N-Jump. Let's take a look at the "D" end of this timeline.
Marty McFly grew up a different person--not drastically different, but slightly different. His family now has money; he doesn't necessarily need Doc to help him put equipment together. However, in this timeline, Doc knows that Marty will go back into the past, and so Doc has an interest in preserving the timeline (remember, he's the one who best understands the temporal problems; given those 30 years, he would have worked out the necessity of Marty McFly returning to the past, interfering with his parent's meeting, and bringing them back together, without which we are caught in a different infinity loop, as those events keep happening and "unhappening" with each cycle). Thus Doc would cultivate the relationship with Marty, hiding the truth about the past from him, so that Marty would return. Doc has also read Marty's note, and recognized that in order for him to save his own life, 1) he must take some steps to prevent the Libyans from killing him, and 2) Marty must believe that he was shot. The bullet proof vest is the best answer. Marty--the more affluent Marty of the C-D timeline--sees Doc shot, and escapes to the past, not knowing that Doc was wearing the vest. Still concerned for his friend's life, Marty still writes the note, so Doc is still saved.
But the Marty who returns from point D reaches point E--not point C nor point A--because his information is completely different. In his history, George's friend Marty was trying to get George together with Lorraine, and Biff got in the middle, so George K.O.'d Biff, impressing everyone, especially Lorraine, who danced with him, kissed him, and married him--living a very different happily ever after than the one in the A-B timeline. This Marty, the one born and raised in the C-D timeline, knows nothing of George being hit by a car. He (and Doc) have a lot more extrapolation to do in order to realize that Marty is the Marty for whom he is named--the friend whose influence helped bring them together, the friend who encouraged George to share his stories and become an author, and then disappeared after the Enchantment Under the Sea Dance, never to be seen again. And so the E-F timeline is in some ways different from the C-D timeline which we saw. We have a sawtooth snap; history repeats itself until either it falls into an infinity loop (by a change drastic enough that Marty cannot return to the past) or advances to an N-Jump termination (in which Marty's next return to the past will repeat the previous one in every detail).
Clarifying this, if Marty on this E-F timeline fails to bring his parents together, then at F he no longer exists, and we return to the A-B timeline, forever trapped in an extended loop. If he fails to interfere with his parents' original meeting, then at F we have restored most of the circumstances which existed at B, and the other Marty will make the time trip to set up the C-D timeline. If he succeeds in bringing about the same results as the C-D timeline, then history continues as at the end of the movie--except of course that the Marty who wakes up in the upscale McFly home is not at all surprised, because things are as they were when he left.
However (one more minor complaint with the first movie), the Marty McFly whom we see at the end of this film does not exist. Although he returned before he left (creating a minor N-Jump--he changed nothing of significance by doing so), at the moment that his other self leaves for the past, that timeline is erased. The only future which exists is the one at the end of the E-F timeline. Remember: for the Marty McFly who is seen leaving by the Marty McFly who has just returned, that more affluent existence, that altered history we just watched, is his. He is not the same McFly. And when he returns, he will reach point F, the end of the timeline he is on his way to create.
That timeline will be different, but it is possible that the end will be much the same (without the surprised Marty). Doc will have his bullet proof vest (a gamble, as he did not know that they would not shoot him in the head or use armor piercing bullets), and so will be alive, if somewhat bruised. His family might be the affluent version. And since it might be so, and the story continues that it is so, it is reasonable to conclude that on the last timeline of the sawtooth snap--whether it is E-F or Y-Z--time continues into the affluent future. Back to the Future, in its first part, allows the future to continue.