The simple answer is the throttle blades open and allow more air in, but there's a lot more to it than that.
You have to realize up front that an internal combustion engine (ICE) is nothing more than a big air pump. Air goes in, mixes with fuel, gets compressed by the piston, the spark plug lights the mixture forcing the piston down, which rotates the crank, which creates power. The burnt air/fuel (now exhaust) is routed out of the engine and through the exhaust. This is called the Otto Cycle and is the basis of all four stroke engines.
When the foot steps on the pedal, one of three things can happen, depending on what type of engine management system is in place.
If drive by cable (DBC) with fuel injection, the foot steps on the pedal and the pedal moves a cable, which directly moves the throttle plates inside the throttle body. A mechanism called a throttle position sensor (TPS), which then tells the computer how far the throttle plates are open, which it then commands the injectors to fire a predetermined amount of fuel into the engine, which mixes with the incoming air. Then the spark plug goes off at the right time and things start to happen.
If drive by cable (DBC) with a carburetor, the cable opens the throttle plates, which allows more air to enter the engine. The incoming air which rushes through the venturis of the carburetor which allows air/fuel to mix, which enters into the engine. Then the spark plug goes off at the right time and things start to happen.
If drive by wire (DBW), the foot steps on the pedal and the pedal reacts with a rheostat, which tells the computer the amount of movement of your foot. Then the computer commands the throttle body to open the amount required to match the command. A motor in the throttle body then rotates the throttle plates which allows the amount of air into the engine to do what is required. The computer also commands the injectors to fire a certain amount of fuel into the cylinders, which mixes with the air. Then the spark plug goes off at the right time and things start to happen. (NOTE: There is no carbureted version of DBW. This is fuel injected only.)