Fingerprints are a way to differentiate an accidental "hit" during a background check, in the event your vital information matches or closely matches a known felon. If a background check is performed on you and your personal data closely matches someone with a criminal history (not uncommon) or known "wants" (warrants, etc), then further investigation is required.
The fingerprints can be used to verify that the subject is or is not the same person verified by checking positive for criminal history ("III") or a wants check. This is also done with physical description, but every detail concerning you will be used to verify who you are to avoid cases of mistaken history or identity.
The NCIC database isn't filled with the fingerprints of every person who has ever had a background check. The database is not yet complete, but includes those with criminal histories or known wants at the federal level (and some states). Accordingly, when you submit for a background investigation, you aren't becoming a file somewhere; you're simply being checked against a known file of criminals.