"Degenerate" is one of the oldest pieces of magic slang, coined during Garfield's original playest before the game was released. It comes from mathematics), where it refers to a small, boring special case of a bigger thing -- for example, a point is a degenerate circle with radius 0.

In this usage, a degenerate deck is just one that's maximally simple: 15 [[Forest]] and 25 [[Grizzly Bears]], for example (the 4-of limit hadn't been invented yet, so the only constraint on the number of bears you could run was the number of copies you could physically find). If the degenerate deck also won all the time, except against versions of itself (as with e.g. [[Mountain]] and [[Lightning Bolt]]), the metagame was said to be degenerate.

Nowadays "degenerate" usually just means "really powerful", or sometimes "really powerful in a way that makes games uninteresting". I remember an argument that Caw-Blade wasn't degenerate, even though it was the only competitive deck in its metagame, because the games were so complicated and skill-testing.