A body pillow is a long pillow that you can rest your body alongside, to snuggle up to or just sleep on. At their smallest, they are four feet long; I'd estimate the average one to range from five to six feet in length. The 'normal' form is essentially a 'stretch pillow' - width and thickness are the same as an ordinary pillow, but it's longer. In catalogs they are depicted almost without fail with a woman asleep on her side facing the pillow, arm and leg on the pillow, with a faint smile on her face.
Of course, there are other variants. The fish pillow version I mentioned would be one. One variant I haven't seen anywhere but in a airplane catalog was one that was long enough to wrapped around, so that the user was surrounded on all sides, with a headrest as well. That variant would be ideal for nesting.
My wife was a fan of them before we were able to live together -- according to her it's fairly close to having a body next to you while you're sleeping, and it won't steal the blankets (though it won't be warm either). They can be nice when you're trying to arrange your blankets and pillows to get that perfect 'nest' effect to sleep in.