The common use today, at least in Canada and the U.S., is when it's used an an adjective to mean something that is trivial and not worth considering. You've heard of the expression, "It's a moot point". Well, it means that said point has little or no practical relevance - it doesn't matter.
Example: Saku and Alfie arrived at the concert late, which caused them to miss the opening act. It was moot arguing over whose fault it was since neither of them could travel back in time to get to the concert earlier.
However, moot does have another, albeit rarely used definition. In fact, it can mean something that is debateable. Historically, moot was used as a noun meaning an assembly held for debate.
*Segue into Lord of the Rings*
In the book/movie, Lord of the Rings, there are giant talking trees called Ents. In the Two Towers, the Ents convene an Entmoot, a gathering or meeting where they decide/debate whether or not to join in the fight against Saruman, whose armies are cutting down large numbers of their trees.
Who said you can't learn anything from fantasy novels?
I've heard people say "mute point", which makes me giggle inside because if their point is mute, I can't hear it. The error is easy enough to make, though. While moot is pretty uncommon, I can see why people would interpret it as the more familiar word mute. Simply put, mute means silent, like the volume on your TV. It can also describe the inability to speak.
Check out a clip from Lord of the Rings: The Two Towers, where the Ents end their Entmoot with a decision.