Why do detectives look for fingerprints at the scene of crime?

Fingerprints can be analyzed and used to identify a certain individual that has that fingerprint.
Each persons fingerprints are unique to that specific person. The perpetrator of a crime may be
identified by fingerprint (s) left at the crime scene.

Fingerprints are unique to you. If they are found at a crime scene, it is fairy certain that you have been there. Of course, there may be a legitimate reason for you to be there, but it's a start for eliminating suspects.