A wormhole is a path through curved space that can connect two places in spacetime. To simpify the idea, imagine a universe that is only three dimensional instead of four. Think of two dimensional beings that live in the three dimensional universe. To them, everything would be flat. But say their universe is curved so if we (who CAN observe three dimensions) looked at it, we would see a sphere. So if one of the beings starts walking from one spot, eventually, since the universe is curved, the being would travel all the way around the universe and end up where it started. To us, this seems reasonable because we are used to such 3D phenomena such as a sphere, but to the two dimensional creature, it would appear very strange because the creature would have percieved that it was traveling in a perfectly straight line since it cannot detect the curvature of it's universe. This is how it is with the fourth dimension, which we call time. Imagine again our three dimensional sphere universe. Let point A be at the top of the sphere, and point B be at the bottom. Keep in mind that I use the terms "top" and "bottom" loosely since to the two dimensional creatures, these points would simply be two different places on a flat plane because they cannot percieve directly the curvature of their universe. To them, the shortest distance between A and B is what is to them a straight line through curved space. So taken from a 3D perspective, their straight line is actually a curved one which runs from the top of the sphere to the bottom. You can directly observe this affect by drawing such a line on a ball and looking at the ball head on so the line appears to run straight from top to bottom. Rotate the ball along the Y axis a bit, and you can see how the line is really a curve. So what would the shortest distance really be? it would be a straight line from A to B, but it would not travel along the surface of the sphere, but would run through the interior of it. So to us what is a true straight line, would be to the creatures, a wormhole.

A very easy way to see the two dimensional wormhole is to take a normal sheet of paper and draw two points on it. One point at the bottom right corner, and one at the top left. When the paper is flat, then the shortest distance between these points is a line that crosses diagonaly across the center of the paper. But, if the paper is curved (as the universe is), then we can fold the corners together so that the two parts of the paper touch. Then the shortest distance between the points is through the paper and hence shortened significantly.

So increase the dimension count by one, and you can get an idea of how a wormhole might work in our universe. What to us is a straight line through space, might be a curved line through four dimensional spacetime. So how could a wormhole exist? Well, imagine a singularity like a black hole. The area of spacetime around the singularity would be extremely curved because of its gravity, so if an area of the curved spacetime connected with another, far away area of spacetime, a shortcut would be created - a wormhole.

I hope this helps.