In simple terms, it’s the idea that the universe started in a hot dense state and has been cooling and expanding ever since.
This is, alas, one of those topics where everyone, even people who have never seen the inside of a physics classroom, thinks they know all about it, and for whatever reason it attracts cranks and wooagers like flies to hamburger, but it does not say what most people think it says. In particular:
- It was not an “explosion.” It was given the name ‘Big Bang theory’ derisively by a person who didn’t want to accept it. Its formal scientific name is the Lambda-CDM model.
- It does not say the universe “came from nothing.” Creationists who are utterly ignorant of science, physics, and cosmology trot this out all the time. The moment anyone tells you ‘the Big Bang theory says the universe came from nothing,’ that’s your cue to tune them out and discard everything further they have to say. They aren’t educated enough to be worth listening to.
- It does not describe how the universe started. The Lambda-CDM model only turns the clock back to the Planck epoch; it describes the expansion of the universe from a hot dense state. It does not go back to the moment of the creation of the universe; we can’t model that because we don’t yet have a quantum model of gravity.
Condensed to its essence, it’s a model of the progression of the universe from a very hot, very dense state to the sparse, cold state we see today.