It's like a baritone. I've heard many different descriptions of these two astonishing instruments. A euphonium is much like a small tuba. The both come from the same family. The euhponium is a brass wind instrument about 3 feet long and sometimes silver plated.
Euphoniums are usually bell up instruments, as seen in the picture.
In normal four valve euphoniums, the fourth valve is alongside the other 3 valves. The only compensating horn that I've know to have the fourth valve besides the other three is the Canadian Brass insturument, a small production line put out by Wilson. Baritone horns are much like euphoniums, though they are a tiny bit smaller, lighter and have a sharper brighter sound. The baritone was invented after the euphonium, mostly, I believe, for marching purposes. Most baritone horns have the bell curved forward to help project the sound.