It was during the 1920's that Edwin Hubble provided the first evidence that we live in an expanding Universe. Hubble discovered that there is a simple relationship between the distance to a remote galaxy and the redshift in the spectral lines from that galaxy. This redshift is know as the cosmological redshift. Hubble's observations showed that the greater the distance to a galaxy, the greater the redshift in its spectral lines. These measurements strongly indicated that galaxies appear to be moving away from us with speeds proportional to their distance. This observation is made in whatever direction you may look in the sky, giving the (false) impression that our solar system is at the centre of the Universe. The net effect of this motion is that as time goes on the galaxies are getting further and further apart. Astronomers describe this as an expanding universe.
A very simple analogy may be drawn with the blowing up of a balloon on which a number of reference points have been marked. The balloon is illustrative of the Universe and the reference points galaxies. As the balloon is inflated each reference point moves further away from the other, so from any reference point within the balloon every other reference point appears to be moving away from the observer. The observer does not have to be at the centre of the balloon to make this observation. Where this analogy breaks down is that, on the skin of the balloon the reference points will expand, as well as the distance between them. In the Universe the expansion takes place in the space between the galaxies. The galaxies themselves do not expand.
A very important consequence for observations which lead us to infer an expanding Universe is that at some point in the past the matter which is becoming increasing distant must have been concentrated all in one place. Astronomers believe that at this point in time, the beginning of the Universe and the beginning of time, all the matter of the Universe was concentrated in an infinitely small volume and was in a state of infinite density. This time can be calculated by a number of different methods. [For further details see the section on the Age of the Universe.] The huge explosion which led to the expansion of the Universe is the event known as the Big Bang.