A bodice is the upper (torso) section of a dress or gown. It covers the upper body and supports the weight of the attached skirt. It may be laced up at the front, side or back, buttoned, or closed with hooks and eyes.
In period, a "pair of bodies" referred to a corset, that is to say, a feminine foundation garment worn over the smock/chemise and under the gown -- never outerwear. Historically speaking, the separate bodice and skirt as outerwear probably did not appear until the very end of the SCA period.
In modern parlance a bodice may also be an item of outerwear, often worn with a separate skirt and chemise. In the more demure cases it extends up towards the neckline, framing the chemise; in the less demure, it tends to exhibit the bosom. This look is popular with Renaissance Faire-goers and self-described "wenches".