The Big Bang theory tells us how the Universe began and is evolving. In essence, it is a theory that was created to explain two facts that we know about the Universe - it is gradually expanding and cooling. In the 1920s, Edwin Hubble found that galaxies far from our own Milky Way are moving away from us. In fact, the further away galaxies are, the faster they are receding. So he concluded that the whole Universe must have been expanding. Working backwards this means that at one stage the Universe must have come from a single point.
We also know that the Universe is cooler now than in the past. In the 1960s Arno Panzias and Robert Wilson detected the afterglow of the Big Bang, known as the cosmic microwave background [or CMB for short], which revealed that the Universe was once a very hot, hostile place. Both these discoveries led astronomers to deduce that the Universe began as an infinitely compact fireball.