A body brush is a soft bristled brush that, as its name suggests, is designed to be used on the "body" of the horse. However, the bristles are soft enough to use on the head and legs. Some people also use the body brush to brush out the mane and tail as they believe a comb will thin the hair. (Some people also use the kind of human hair brush that has the thick plastic "knobs" instead of bristles, which works quite well on tails).
Like the dandy brush, the body brush can come with natural or synthetic bristles. A lot of people who have synthetic dandy brushes will pay the extra for natural bristles on the body brush. More expensive body brushes have leather backs/handles.
The body brush also sometimes has a strap on the back to insert the hand through. It's used to do the real work of grooming, remove fine dust and add shine to the coat.
(I apologize for the lack of good images. I can't find any, oddly enough).