I too am intrigued to know more about this, especially for my school of choice - Tuck.
As far as I know, background checks are done to verify:
1) Periods of employment at each firm
2) Whether the designations and time periods you have indicated on your resume are correct
3) Whether those who recommended you, know they recommended you - i.e. you didn't submit a recommendation yourself on someone else's behalf
4) Your education details are accurate
Credit checks are not done for international students. In fact, until a couple of years ago, there was no public credit rating system in India for example.
What I have also heard is that this is a standard process and doesn't do any harm. If there are minor deviations from your resume, that is OK. A red flag, a proper one, should not go up - that's all that is being checked. I haven't read about someone's admission offer being rescinded due to a background check.