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First it is important to know where the name wormhole comes from: It is a methaphora for a worm eating its way through an apple. When it comes out of the other side, the worm connects both sides of the apple with a tunnel.
You have to imagine a wormhole just like the tunnel the worm creates. The only difference is that wormholes create a shortcut from one point in space to another one. And this phenomenon works like this: theoretically you enter a wormhole, and instead of just travelling through it, you 'roll up' huge distances by travelling with the mouth (the place where you enter and leave a wormhole) you have entered to the mouth you probably will come out. If scientists wanted to build a wormhole, they would need a lot of exotic matter, a kind of matter with negative mass that has to be produced first. At the moment it would theoretically be possible to build a wormhole with a diameter of half the radius of an atom. If they wanted to create one with the diameter of one metre, they would need a big amount of exotic matter, as big as the mass of Jupiter.
There are theories of different types of wormholes, for example there is a theory by Stephen Hawking, that there is a kind of wormhole – a flat wormhole – that allows you to go through it and come back just to the time and place you have entered it. There are three other kinds of wormholes:
1. Traversable wormhole: This would be a wormhole which matter is able to 'travel' through.
2. Intra-universe wormhole: Connects two locations of the same universe (in the present, in the future or in the past). In the case of an intra-universe wormhole, the wormhole would create a shortcut from one point in space and time to another. This possibility would also create the opportunity of time travelling.
3. Inter-universe wormhole: Connects one universe with another one. Also called Schwarzschild wormhole or Einstein-Rosen-bridge. They are not traversable and their mouth can be held open with exotic matter. This kind of wormhole could theoretically be used to travel to parallel worlds.

This picture shows an inter-universe wormhole and the bending of time around it. The blue area shows the mouths of the wormhole, and the purple area shows the throat of it.
Unfortunately it is impossible for a traveller to pass through a wormhole, because when you enter it, it collapses immediately. This effect is caused by the gravity of the wormhole itself, so even if there is only an atom passing through its mouth, the throat will collapse, hence you are not able to reach the other side. And there is only one way to stabilise it: exotic matter. But here we are facing the next problem: the high energy consumption to produce enough of this matter. Is this the end of the dream of interstellar travelling?
Read on (in German): Website
of TTRC
Images found at Wikipedia and http://www.onteora.k12.ny.us/Onteora/lib/Onteora/_shared/various%20graphics/worm_in_apple.jpg.