Transistors are a basic building block of electronics. You know how electrons, protons, etc are the building blocks of matter? Transistors are like that for electronics. All digital electronics are made of transistors. They have numerous uses but for understanding the operation of the 555 we just need one: a switch.

The 555 uses a transistor as a switch to connect part of the circuit to ground:

When the line labelled controlgoes high, the transistor turns on and connects the circuit it's connected to, to ground.

In the 555 this is used as the mechanism to discharge the timing capacitor.