It's a digital representation of a given speaker cabinet ... or an environment, such as a room or instrument body. Just as the raw guitar sound is shaped by the speaker it is amplified through, instruments played through impulse response curves are shaped as well.
To create an impulse response curve of a cabinet -- in this case my own Hard Truckers 2X12 loaded with JBL E-120s, the cabinet is mic'd with a microphone with as flat as response as possible, and a loud sine wave sweep covering the entire audible frequency range is recorded. The sweep goes from low to high then high back down to low.
The resulting WAV file is then convolved (measured) and the resulting impulse response curve is created. When any sound is played through that curve, it's as if the sound is being played through the cabinet itself and recorded with a flat microphone.
(Note that you could use a Sennheiser 421 to mic the E-120s when you're capturing the WAV file and get a very accurate representation of Garcia's sound; I didn't do that because there are several rolloff settings on the 421 and I have no idea how it was set up when Garcia's cabinet was mic'd.)
It's impressive technology ... when I made the curve of my E-120s (and also of my 2X10 with K-110 speakers), I loaded the curve into the AxeFX and took a stereo output off of there, feeding one side, panned with the curve, into my QSC K-12 full range powered monitors, and the other side into a power amp and the original 2X12 cabinet, without the curve applied. I played through both sides, muting one then the other, and it was pretty much indistinguishable from the original. Same with the K-110s. Made a believer out of me.
Any Playing Dead recording you listen to from mid 2009 or so on is my guitar through an impulse response block in the AxeFX instead of a cabinet. On my Garcia preset, the cabinet IR block is last in the signal chain before it goes direct to the soundboard and my powered monitors.
You might be able to hear the difference in a room with just the guitar, because the inherent characteristics of a 2X12 open back cabinet and the resulting room reflections are going to be different from a sealed full-range wedge sitting on the floor aimed at your face, but in the mix and the context of the band it's extremely difficult to discern any difference.
It would be very interesting to obtain a multitrack recording of 94-95 Grateful Dead concert and then run Jerry's recorded guitar signal into the AxeFX through just the E-120 curve and see how it sounds. If anyone is aware of an extended Jerry "noodle" between songs with just his clean guitar off one of those soundboards, I can give it a shot.