A transistor is just a switch that can be on or off. The original computers used giant valves that could be opened or closed.

They are an electronic component in their own right and not specific to computers.

Combine them with resistors and you can make logic gates (and, or, not, etc) combine these and you can make even more complex things.

So a transistor on its own can either hold a charge or not. It doesn't do anything useful until you combine them with other things.

I would look up videos about how microcontrollers work as they are way simpler than CPUs but the same principal.