Your amp is where everything gets louder. In effect, the amp takes the signal from your guitar and translates it back into sound waves in the air that your listener can hear. But even at this seemingly final stage, plenty more happens to your sound than just the "gets louder" part of the equation.
The circuitry within most guitar amps contains several stages that shape your guitar signal in a variety of ways, one after the other, allowing you to alter and enrich your guitar tone, above and beyond merely amplifying it. After your signal goes in through the input in the front of the amp, it hits . . .
A preamp stage: This stage increases its strength and also, in some cases, adds some slight distortion that enhances its texture, the way an overdrive pedal does. Many amps have multiple preamp stages.
A tone stage: This stage alters the signal's frequency content somewhat, according to how you set this stage's controls.
An output stage: Here the signal is ramped up even further, ready to be pumped through an output transformer that blasts it through the speaker, but where additional body and texture is also added.
A speaker: The speaker pumps the signal back into the air for you to hear, and it also adds some of its own sonic character to everything that has come before.