Can someone explain NYPD ranks to me?

Actually promotion in police depts. do not move much. Generally you start as a police officer in uniform. Then the Detective track starts at What would be the Corporal level. To be a Sergeant or above requires testing & openings for a new supervisor to fill. Benson's character 1. Has never pushed for promotion. 2. In 15 years has made enemies in the NYPD that would reject her moving up. 3. SVU is a small unit VS. other detective sections like Robbery or Homicide.

Detective Sergeant is actually hard to make and there are not very many of them, usually just one to a unit. Police Lieutenant is very difficult to achieve and requires more politicking than most can handle. The rank structure is not the same as the military, but a Patrol Sergeant basically equates to a Sergeant in the military. Detectives have leeway in their investigations and are basically autonomous within a certain degree. Officers follow orders and patrol a specific beat. Detectives are sometimes promoted from the officer ranks, but it usually takes a degree for that to happen. Being demoted from Detective to patrol usually does not happen because if a detective screwed up that bad, they would usually just be cashiered or put on suspension until IA was done with them. For the most part, the stuff you see on TV is real enough to be believable. I suggest you follow that link provided and gain some real edification.

Try the Law Enforcement & Police section

Its amazing how much info Google will give you.

http://nypd.wikia.com/wiki/NYPD_Uniforms_and_Ranks