BugSplat is a crash reporter. A crash reporter is a piece of code that helps developers find when, where, and how frequently their software crashes while in use.
If you saw a BugSplat after your software shut down unexpectedly, it means that the developers behind your software are dedicated to its quality. And that's an excellent thing.
As part of the BugSplat program, the bugsplat.exe file is vital for getting the crash reporting tool to work correctly. Uninstalling the actual BugSplat file is not an option, as it is part whichever program you were using that just crashed.
The best way to fix a program which is crashing is to follow these instructions here, or contact the makers of your software program.