There may be minimum or maximum prices that can be charged.
Some economic actors may be prohibited from entering the market.
Actors who buy or sell on such a market often have to respect additional rules. They may have to pay taxes, and they must respect laws to fight discrimination, and to follow certain labor laws.
There are often reasons why markets are regulated:
Sometimes, there are high barriers to entry, which is the case for telecommunications or energy systems. This will lead to what are called natural monopolies. The regulation occurs to make sure that the market players do not have too much power
In many parts of the world, the state subsidizes certain products. Very often, this is about agricultural products. The price a producer gets for a liter of milk is fixed, or it varies only slightly. This mean that the prices for dairy products in the stores are more or less stable.