I assume you mean FFXIII-2 since that's the one with time travel. There's nothing confusing about it. The main antagonists changed time and thus started a chain of paradoxes to occur which caused the timeline to decay. The heroes simply had to correct the timeline.
Don't think of time as a single line. Think of it as a web. Every connecting point on that web is a major point in time. The strings in the web come from each point based on what happens in that point. If you change the details of the point, you change the strings. You end up creating strings that are unable to properly attach to the rest of the web. The strength of the web decreases, the strings themselves fall downward instead of connecting to other points, and the web itself completely falls apart.
In the web version of time, temporal paradoxes would be changes to those points. By changing one point, you'd affect other points that themselves would change and create more malfunctioning strings and so on and so forth until the timeline falls apart and everything ceases to exist. This is what happened in FFXIII-2.