What is the meaning of [It ain’t over till the fat lady sings]

Nothing is irreversible until the final act is played out.

Just to get this out of the way before we start: is it ’til, till or until? You can find all of these in print:

It ain’t over ’til the fat lady sings
It ain’t over till the fat lady sings
It ain’t over until the fat lady sings

You might even find versions with isn’t instead of ain’t. Grammarians argue about ’til and till; I’m opting here for till.