So... seriously, what's going on with the different worlds?
Before we explain anything we need to get this out of the way. At the center of BioShock Infinite is the mind-bending idea that there are multiple worlds simultaneously coexisting, each blissfully unaware of the others. The idea in its simplest form can be thought of as a tree. Every time someone makes a choice, two new branches are added to this hypothetical tree. Each of these branches follows a path in which the outcome of that choice is different.
As an example, when you woke up today and walked into your kitchen, did you decide to eat breakfast or skip it? Let’s say you decided to eat breakfast. At that moment, an “alternate universe” where you chose to skip breakfast--another branch on the tree--is created. You can’t see this “branch” or even know for sure if it exists. Likewise, the version of you in other branch don’t know you exist. In this world, you may have been late to work as a result of stopping to eat, which led to your firing. In the alternate universe, you were on time and received a promotion. Both universes are “real” to the people living in them, and they never, ever, ever intersect. Well, unless there's a tear.