[summary: A sample space is the set $~$\Omega$~$ of possible ways that a part of the world might be, as far as you know.]
If we are uncertain about some part of the world, then there are multiple different things that might happen there, as far as we know. The sample space for a part of the world is the set of things that could possibly happen there. We can use a sample space to reason using probability theory, so that we assign probabilities to [event_probability events] in a consistent way.
A sample space is a set, usually denoted $~$\Omega$~$.
[todo: examples] [todo: further points]