An electric guitarist usually has a pedalboard that they use to make different guitar tones. Let's approach this like an electrical engineer might.

Time is a straight arrow: call it t.

The guitarist plays, and their guitar pickup records a signal. At any time t, measure the value of this signal's waveform: call it x.

That signal can go into a pedal that maps each value to create an output signal. Call it f(x, t).

The pedal is a linear system when it satisfies f(x1 + x2, t) = f(x1, t) + f(x2, t). In English, you can blend two guitar signals going into a single linear pedal, and it will sound the same as if you used a separate pedal for each guitar.

The pedal is a time-invariant system when it satisfies f(x, t1) = f(x, t2). In English, a time-invariant pedal does not warble over time.

The magic happens when a system is both linear and time-invariant. These systems are so special, we call them "LTI" for short. Feed an LTI system a single, really loud, POP! Something like a clap, or a gunshot. Record the sound of this gunshot, and call it "impulse_response.wav". This file characterizes EVERYTHING about the system. If you know how the system responds to an impulse, you will know how the system responds to any other sound. All you have to do is convolve the sound with the impulse response, i.e. use the contents of impulse_response.wav as a set of weights and pass the sound through it.

The echoes you hear when you speak in a large room is a real-world example of an LTI system. People will go to a cathedral, an open field, or a large tunnel, set up a microphone, and fire a blank pistol. They can go home, convolve the sound of their guitar or voice or whatever with the impulse response, and it will sound exactly like they're in that space! There are whole communities of people making and sharing impulse responses out there, and I just think it's the coolest thing ever.

For any guitarists reading this, I'll bring this back to the pedalboard. Another cool thing about LTI systems is that when you chain multiple of them together, the order does not matter. Reverb, delay, EQ, and wah are all LTI effects. If you've ever wondered why pedal ordering sometimes matters and sometimes doesn't, this is why.