The choke is a slight taper in the last two inches or so of the barrel, to control the diameter of the shot pattern at some specified range. Commonly, this is some percentage of the total number of shot at, say, 30 yards.
The tightest choke is "full". Then, "modified", "improved cylinder" and "cylinder". This last means no constriction at all. Somewhere between improved cylinder and cylinder, if I have it right, is "skeet". Don't quote me on that, and don't ask.
The purpose has to do with the type of shooting one expects to do. For instance, on many double-barrelled shotguns ("double-gun") it is common to have modified and improved cylinder for quail hunting. One finds the quail initially at fairly close range, and shoots with the improved cylinder barrel first. The second bird is shot at, then, with the tighter-choked modified, as he is farther away.
Goose hunters usually use full-choke guns, given the longer ranges typical of that sort of hunting.
There's a start. Check out the archives...
FWIW, Art