In terms of the guitar, an impulse response is a measurement of a sound source, usually a mic’d up guitar cabinet in a room. This ‘snapshot’ or ‘capture’ of the guitar cabinet allows you to take a great tone and use it in any studio, rehearsal room, or live on any stage. It means you can get a classic speaker sound from a 4x12 without using an actual cabinet which is often impractical for home use.
Another example of an impulse response is a convolution reverb, where the sound of a physical space is captured, allowing you to play your own sounds through a room you’ve never actually been in. The theory is the same as the cabinet impulse response, allowing you to play your guitar through a cabinet you don’t own.