The approach is actually pretty simple. There are two parts to it:
1. Arrest someone for jumping a turnstile or spraying graffiti on the side of a building, and you now have the perpetrator's fingerprints to run through a police database of unsolved crimes.
2. Even if the fingerprint doesn't match the records from any unsolved crimes, you now have a new set of fingerprints on record to identify the perpetrator if he ever commits a crime later. There was a high-profile rape/assault case in Central Park back in the 1990s that was solved this way.
3. Criminal laws that are NOT enforced become “gateway crimes” for greater criminality. Enforcement of those laws (nip it in the bud) help make the step into criminality that much bigger.
Best way I could word it, but you get the drift (I hope)