In a discussion of time travel, questions will come up about freewill and causation. I have always found this conversation frustrating because the common view is just so plainly wrong.
The common view is the one espoused in Back to the Future, which arguably is where most Americans get their understanding of time travel. (I guess as opposed to empirical time travel science?) Everyone knows this so I don't even have to summarize it, but here goes: You go back in time but you have to watch out that you don't accidentally change anything, because if you change something because then you will change the future. In particular, you need to make sure that your introduction to your parents when they were in high school doesn't keep them from falling in love, or else you would undo your own existence, the fact of which alone should point out that there is something screwy here.
In this idea, because you can change the future you came from, there are different "timelines". When you go back in to the past you go to a different timeline or split the universe or whatever and the effects of your meddling will be in the new timeline and not the one you came from.
So why do we think there are multiple timelines?