Hello my name is Bradford and I'm an Independent Advisor for the Microsoft Community and I will try to answer your question.
A "fault bucket identification number" is a number assigned by the system to identify specific types of errors.
This number is used by Microsoft to identify a particular program error when you send an error report.
If you get a "this program has encountered a problem and needs to close" type error, click the 'Send error report' button, and you may get a resolution to the problem.
Also, you can search via Google using the specific Fault Bucket ID Number to possibly find more information about that specific error.
I hope this answers your question.
Finally, if you don't mind-please click the "Yes, this was helpful" button if this was, well, actually helpful :0)