For me an amp which is fast is one in which the leading edge of a note (burst of sound) rises from nothing to full reproduction in a very short time. Think of a graph with a flat line which, when there is a burst of energy, can move perpendicular to its original path, i.e. 90 degrees (which would be as fast as it can get) or could rise on an lesser angle which would make a duller sound. (The correlation to rise time is how long it takes an amp(and speaker)to release a sound, i.e. damping). An amp which is fast can greatly enhance the sense of pace and rhythm of music if your speakers are up to it.