Using sophisticated DSP (Digital Signal Processing) it is now possible to emulate an almost infinite range of amplifier and speaker combinations. Complex algorithms have been designed to give a truly realistic sound which simulates the result you get from a mic'd-up cabinet. Some of the higher end products even let you vary the microphone position relative to the cabinet, and even the microphone type itself to give you ultimate control. This can then be fed directly to your DAW, PA or a regular guitar amp.
Amp modellers generally have a selection of different amps and a separate selection of speaker cabinets to choose from. The combination of these amp and speaker simulators, together with careful EQ and FX settings can give a sound which in the past has taken guitarists literally years to achieve through experimentation with various amp and speaker setups. Most models offer a variety of presets to get you started, and some even have the option to download extra pre-sets based on famous guitarists signature sounds.
As the modelled tones are created to emulate the effect of amps being driven hard (which is when most amps sound at their best) guitarists can now simply plug-in and play without having to turn up the gain to '11' just to get the desired sound.
More and more artists now rely on the convenience and killer tones of amp modelling, including Steve Vai, Ed O'Brien (Radiohead), James Hetfield (Metallica), The Edge (U2) and many more.