These are log files the game generates when an 'exception' occurs inside the game while you are playing (no matter if you see something strange happen or not). They contain text, information that can be useful for The Sims team under certain circumstances. For example, we might ask you to share one of these files with us when you are reporting a bug if we think the information can be useful for that particular issue you are telling us about.
But you don't need to worry about the LastException files. You can safely delete them if you want, it's also ok leaving them be where they are. :)