What is a simulator program in car racing games? What are the hardware requirements? How are they connected?
You ask the question as if they are two different things. A car racing program, a flight program, etc are all simulators. A simulator is any computer program that models the real world.
This depends greatly on which game you're talking about and which platform it was developed for. Game developers use game engines which compute certain things for them, such as gravity, artificial intelligence, physics and so much more.
These engines are almost whole heartadly responsible for the realism (or lack there of) that your game embraces. The better engine that is used, the more realism you see. Although not always true, this is usually the case. Other components such as modeling software and particle systems play roles in the game, but are usually included in the engine.
The simulation you speak of, is the engine trying to recreate reality to its knowledge (i.e flying around a corner causes you to flip, since the engine knows that at x speed, making a turn of more than x degrees is going to cause a flip).