Going out with a bang

Need some help with "going out with a bang". What does this mean? Where does it come from? Thank you in advance.

T. S. Eliot "The Hollow Men" concludes,

This is the way the world ends
This is the way the world ends
This is the way the world ends
Not with a bang but a whimper.

"To go out with a bang" probably predates Eliot, but I couldn't resist the urge to quote him.