A common misconception is that the Universe started out as a speck that exploded, creating the cosmos as we know it. During an explosion, objects are thrust outwards from a common centre. Now, we see all galaxies receding from us in the same way in all directions, which – if caused by an explosion – would mean we were at its very centre.
However, any extraterrestrial observer anywhere else in the Universe notices galaxies receding in the same way, as the Big Bang was actually a rapid expansion of space-time. While already being boundless in size at the beginning (except maybe at an initial singularity), space-time is increasingly being stretched out like an infinite rubber sheet. In the same way that any dots drawn on such a sheet move apart in the process, the separation between galaxies increases as the Universe expands. This expansion is still going on today, and, as observations suggest, at an accelerating rate.
Bonus round: An important thing to remember is that the Universe does not expand into something else. There is nothing ‘outside’ the Universe; it is all there is.
Big Bang, Universe, Black hole
World news – GB – Myth debunked: The Big Bang was an explosion