Its such a simple question, that's its actually quite complex. Sometimes the most basic info can delve into the most fundamental aspects of a complex system.
Ever heard of a pre-out voltage rating on a h/u? As in, 4volt pre-outs? This is the signal strength sent through the RCA cable in volts. But, this rating is only at full volume. The way you actually control the volume of your stereo at the h/u is by altering the voltage the h/u puts out to the amplifiers. The higher you turn up the volume, the higher the voltage in the signal cable is.
An amplifier can be described, in basic terms, as merely a 'gain block'. This means it takes the voltage of the signal, and increases it ("amplifies" it) by a fixed amount. But you are saying to yourself "wait a minute, the amplifier clearly alters how much power is sent to the speaker"... this seems elementary, but is actually a backwards way of understanding what is happening. The amp manufacturer has no way of knowing if you will use a h/u capable of a 1/2volt (maximum), or 8 volts, or anything in between. So the manufacturer puts an input sensitivity adjuster on its units, called the gain knob.
Contrary to popular belief, amplifiers always 'work' at the same intensity. Imagine you are rolling a rock up a hill. You always push with the same force (your strength does not change). Now imagine, if the rock is smaller, you will be able to push it faster than if the rock is larger, again because your pushing force never changes. In this parallel, your strength (pushing force) is the amplifier's force/amplification, the size of the rock is the the signal strength, and the speed of the rock rolling is the end result power applied (friction would be the impedance, which we will ignore in this example for simplification). The amp maker does not know how big the rock will be, but its shooting for a fixed speed up-hill (in watts). Again the gain knob is the adjuster to account for different rock sizes. Clipping the amp would be akin to pushing the rock faster than the sensitivity allows, and over exerting your muscles would be like clipping the signal.
As you adjust your volume knob up and down, its like making the rock smaller or larger. The speed increases or decreases as you turn the volume up and down, altering the power output, even though the amplifier's 'pushing force' never changes. The amp's exertion on the signal never changes, but the incoming signal to be amplified DOES change, altering the final work exerted (speed of the rock).
This is not a perfect example, and if you think about it you can find holes in that parallel, but Ive found this usually gives people a good idea of the fundamental things going on in a signal-strength to gain-block situation.
Hopefully that's clearer than mud, Ive had a few drinks this morning (I work 3rd shift right now so this is my night time, dont you judge me! lol).