Here's why:
* Expansion: The Big Bang wasn't an explosion in space, but rather an expansion of space itself. Imagine dots drawn on a balloon. As you inflate the balloon, the dots move further apart, even though they themselves aren't moving across the surface.
* Redshift: Astronomers observe that the light from distant galaxies is shifted towards the red end of the spectrum. This is called redshift and is interpreted as a Doppler effect, similar to the way a siren's pitch changes as it moves away from you. The further away a galaxy is, the more redshifted its light, indicating it's moving away from us faster.
Important Note: The Big Bang theory doesn't say where the universe is expanding into. It's not expanding into an empty space, it's more like space itself is getting bigger.