Convolution reverb (AKA Impulse Response, or IR) is the closest thing to being there, without actually being in the room. When convolution was introduced by Sony on their digital tape machine, the PCM series, it didn't degrade the high frequencies, and people didn't like it. Sony basically invented convolution to emulate what is really happening on an analog machine.
So eventually, convolution made its way into reverb. What convolution does is capture/sample the sound of the room. In order to capture a space you would take a starter pistol, set up a microphone array (it's up to you; you figure out where you want to set the mics up) wait for silence, and fire the gun. Capture the entire sound, and you just created a convolution wav file. The convolution reverb program takes this file, analyzes it, and layers the frequency response on to the direct sound (It's way more complicated than that, but that is the essential process).
Convolution puts a listener in a specific place, at a specific time. For example, say we go to the Taj Mahal in the dead of summer. The air is hot and humid, and we capture the sound. Then we go back in the dead of winter and capture the sound. Think they will sound the same? No, the winter will be brighter since the air is less dense. But you’re also just capturing one instance of the sound. If we fired off 10 pop guns in a row and analyzed each wav file for frequency content, they’ll be different, but we can only pick one file for our convolution purpose.
Convolution has been a godsend to the Foley world (named after Jack Foley who pioneered the art of sound replacement for film). Now as an audio designer for film, I don't have to travel anywhere since almost every car, plane, sound stage, forest, desert, etc has been convoluted. It’s also been a revolution in the guitar world. However, because we are only taking a moment in time, the tail on convolutions tend to not feel right for a music mix. For music reverbs, algorithmic/emulation based reverb tends to sound more appealing.
Algorithmic Reverbs explained in Part 3