To quote from Wikipedia:
"The Big Bang is the cosmological model of the universe, originally conceived to describe its origins, that is best supported by all cosmological observations. The essential idea is that the universe has expanded from a primordial hot and dense initial condition at some finite time in the past and continues to expand to this day. Observational evidence for the expansion of the universe came first from Edwin Hubble's 1929 discovery that galactic distances are proportional to their redshifts. Since the universe is seen to be expanding today, theoretical cosmologists can make detailed predictions of the universe's denser and hotter past. A major feature of Big Bang cosmology is its prediction of the conditions of an early universe having extreme densities and temperatures that today can only be probed in high-energy environments. The results of Big Bang predictions have been found to conform accurately and precisely to a variety of astronomical observations."
Within fiction, a Big Bang is usually portrayed as a massive release of energy, instead of an expansion of space-time itself.
You can watch this educational video for a better explanation.