Wormholes are related to black holes in that they, like black holes, bend space around them into a funnel-like shape. Unlike a black hole, however, a wormhole's mouth is two-way. Once you cross the event horizon of a black hole, you are trapped inside forever. On the other hand, after you enter the mouth of a wormhole, you are not. It connects to another point in space which may be far away from the point you entered, as shown in the figure above.
If you looked through the spherical mouth of the wormhole in the figure, you would be able to see through the wormhole, getting a glance at the light from Vega. The subject of wormholes has been worked on extensively by John Wheeler and his research group in the 1950's, and more recently by Kip Thorne and his colleagues at the California Institute of Technology.
One very interesting possibility that comes up when talking about wormholes is the thought of traveling through time. Since wormholes, like black holes, bend not only space but also time (remember, they are connected in the space-time continuum), this could be possible.