(Please note that much of this article is speculative)
Wormholes are defined as being the hypothetical theoretical connection between a black hole (see Black Holes) and a white hole.

The equations of general relativity (see General Relativity) have the mathematical property of being symmetric in time. This means that you can take any solution to the equations and if you assume that time runs backwards, you can calculate another valid solution. Hence the theoretical existence of white holes.

A white hole is a black hole running backwards in time. It is a location of space-time that instead of being impossible to escape, it is impossible to reach. White holes are theorised to repel everything, including particles and photons, so nothing can enter them. While white holes are a perfectly valid mathematical solution this does not mean that they actually exist in nature. In fact, they almost certainly do not exist since there is no way to produce one (unlike black holes).

A wormhole is often described a sort of tunnel through space, through which matter can pass. They link two destinations in space by tunnelling through space-time. Imagine an apple with a hole bored through its centre. There are two ways to get between the two holes on the surface of the apple. The first is to walk across the surface from one to the other (space) and the other is to travel down the hole from one to another (wormhole). Wormholes are theorised as being able to link two places and hence shortcut the travel.

The white hole that anchors the one end of the wormhole, could be somewhere very far away from the black hole even in a different region of space-time (different universe). Therefore a wormhole could be a convenient and rapid way to travel very large distances or even to travel to another Universe. It could be that the exit to the wormhole would lie in the past allowing time travel (see Time Travel).

Trying to enter a wormhole is theorised as impossible with instant death being the only outcome if it was attempted. Even if a wormhole was formed, the slightest perturbation (i.e. attempting to travel through it) would cause it to collapse. The only way to survive would be if the wormhole was somehow stabilised for a time. This might be achieved by "threading" the singularity with exotic (artificial and unstabilised) matter. However even if this was attained, travelling through a wormhole would be deeply unpleasant. There is a high level of radiation that gets blueshifted to high frequencies. A traveller would be exposed to extreme x-ray and gamma radiation.