The Expanding Universe
Imagine a racing car moving towards you very fast, passing you then moving away from you. To the person driving the car the sound of the engine doesn't change but to you it does. This is because the sound waves coming from the engine are squashed together when the car is approaching you and so the frequency of the sound reaching you increases. When the car moves away from you the space between the waves is bigger so the frequency is lower. This is called the Doppler effect.

When we observe light from distant galaxies the spectral lines are in the wrong place. They are shifted towards the red end of the spectrum, i.e. their wavelength is bigger than it is supposed to be. This is because these galaxies are moving away from us very quickly and the light waves from them are stretched as in the diagram above.
In the 1920's Edwin Hubble discovered that the further away the galaxy is, the faster it is receding away from us, in fact distance and recession velocity are proportional.
Recession velocity = H0 x distance
The constant in this equation, H0, is called Hubble's constant. This relationship shows that the Universe is expanding.
Imagine a balloon covered in galaxies. As the balloon inflates the galaxies get further apart from each other. Look at the distances between galaxies A and B and between galaxies A and C. You should see that the further apart the galaxies are the faster the are moving away from each other, just as in our Universe. This doesn't mean that our galaxy is in the centre, in fact there is no centre. The same would be true no matter what galaxy you lived in.

The fact that the Universe is expanding suggests that in the past the Universe was a lot smaller than it is now, in fact it could have started in one very very space with a BIG BANG.
This is an excellent website about Hubble and his work.
http://www.nyu.edu/classes/gspscience/hou/html/hubble/hubble.html