A wormhole is sometimes described at a connection between a black hole and a white hole.
A black hole, of course, is an immensly dense object from which nothing, not even light can escape, once it has passed it's event horizon. Many suspected black holes have been located in the visible universe.
A white hole is a mathematical prediction from the imaginary number solution of the calculation for a black holes event horizon. (One example of an imaginary number is the square root of negative one.) There are no suspected candidates for these. Apparently there are reasons to not suspect quasars might be white holes. This is an object which repells anything close to it. Nothing can enter a white hole, not even light.
A workhole is the connection between these two features. Black holes almost certainly exist, white holes and wormholes probably do not exist.
So the short answer to your question is: an object would be attracted gravitationally to one end of a wormhole (the black hole) and would be gravitationally repelled from the other end (the white hole.)
Check this out...
http://www.crystalinks.com/wormholes.html
