What shows up when the police run a car's license plates?

Depending on the database the officer is using, he can see if the vehicle is related to any open criminal investigation (for example, has been reported stolen), whether or not the license number is valid, whether or not the registration is current, and whether or not the owner of the car has any active warrants.

Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.