Thank your local electrical company for powering your stereo's speakers. Your so-called amplifier does not amplify. It controls the power of your wall socket. Trivia fact: your wall socket of 120 volts of alternating current could send 3,600 watts into your speakers if not for the amplifier controlling it. The incoming signal to your amplfier is the control signal opening and closing a gate. The power stage of your amplifier limits how much of the wall socket power can flow to your speakers. The power rating of an amplifier is simply the expression of how much power the amplifier can process and send to your speakers before its output stage goes into limitation or distress (or up in smoke.) A higher rated amplfier simply requires higher capacity transformers, capacitors and power transistors to let more of that wall socket power to flow to your speakers.
Interesting point: More power than necessary is often a good thing. If your amplifier is underpowered for your listening habits or speaker requirements the distorted musical waveform created by an amplifier pushed beyond its limits of control can damage speakers, especially tweeters.