Well, when you get a great tone out of a great amp onto tape, the end result is a recorded signal, right?
If you digitize that signal, and you're really smart and know your math and physics, you can examine that signal, compare it to the raw signal thatcomes off a guitar's pickups, and figure out ways to process the raw signal digitally so that it comes out very very close to the signal you're trying to emulate. You basically some up with a set of algorithms to process the signal, and those algorithms constitute a digital/mathematical model of whatever happened to the raw guitar signal in the first place to makje the end result sound so great -- hence the use of the term modeling. It goes further -- they try to emulate the way the bass and treble and mid controls on a given amp effect the end result, as well as what happens to the tone when the amp breaks up, and try their darndedest to mimic all that behavior too with adjustable parameters.
Repeat with six or ten or sixteen or thirty different desirable amps, until you've got a set of algorithms for six or six or ten or sixteen or thirty different models.
Add effects, MIDI control of parameters, put it in a red bean-shaped housing, and call it a POD.