What is an Environment Artist?
An environment artist is a specialized artist that focuses on the construction of world assets for a game or film. An environment artist may build anything from structures to terrain, or even environmental props.
What do you actually do?
I actually do the things listed in the first answer. Specifically exterior structures. On previous titles I have built all manner of assets related to environment art.
What are the general qualifications?
A working knowledge of a 3D application and a good sense of scale are crucial. A good understanding of lighting and architecture are also strong pillars in an environment artist's knowledge base.
What sort of classes (if any) would you suggest to someone interested in becoming an Environment Artist?
Recommended classes for becoming an EA, I would suggest:
www.Polycount.com (good critique can be found here)
www.3dtotal.com (lots of good tutorials)
www.Gamasutra.com (for job hunting)