Rent control, as it exists in NYC, is a damper on how fast rent can rise (both when you're in a lease, and during vacancies of a property between tenants), for people and properties whose income/rent are below certain thresholds where the government considers them to be either paying for or capable of paying for luxury apartments.
Rent control lets you have some reasonable expectation that you can plan expenses for more than a single lease term, as well as attempting to limit how much damage to the economics of the surrounding area real estate prices are going to do (it's a commodity that is hard to increase the supply of in any great quantity, and demand far outstrips supply...this probably would eventually stabilize, but it'd be quite messy in between, and probably not in a net positive way for the city).
Absent rent control, the lower bound of prices would go up, the ceiling would not go down.