Multiple time streams. Long story short, there are multiple timelines with multiple outcomes. Elizabeth is able to manipulate and travel through these timelines to see all of these outcomes. There are an infinite number of outcomes. One of them is Bioshock, one of them is Infinite, one of them is System Shock. If you are having trouble grasping it, think of it like this. You are at a fork in the road. You can go left or right. If you choose to go left, than you forfeit what happens if you go right. [b]However,[/b] there is an alternate universe where you turn right, but didn't go left. Bioshock infinite works around the same concept, except that the fork in the road is when Elizabeth is captured. There also several different points at which he can change his fate, and all of these points create alternate timelines. [spoiler]These points are literal turning points in the timeline, which isn't necessarily a line but more a giant ball of timey wimey stuff[/spoiler] Another interesting thing to note is that not only are his decisions at these moments turning points timelines, but so are the decisions [b]within the timelines created by the previous decision.[/b] TL;DR: Time travel stuff + butterfly effect