@noracodes "every operation is copying" is such a good point, thanks!
so, in a trivial sense, a transmission is just how you get the spinny out of the engine and into the wheels. however, it's often advantageous to be able to change the gear ratios between engine and wheels. (it's called that because if you have two literal gears meshing together, the gear ratio is the ratio between how many teeth they have.)
internal combustion engines really don't like to run too slow or too fast. there's a relatively narrow range of engine RPMs between where they have enough momentum to avoid stalling and where they lose power due to issues with friction, timing, other stuff. by changing gear ratio, you can stay in that range at very different speeds. in low gears, the wheels spin slower than the engine crankshaft; at high gears, they spin about the same speed or faster.
that said, mathematically, power is force times speed. the same RPM in a higher gear will provide less force to move the car.