Taking something too far. Most things only go to ten.
Spinal Tap always took the volume of their music too far. Most amplifiers can only be turned up to ten. Spinal Tap's amps went to eleven, and thus were louder than normal amps.
One might ask why they didn't simply call eleven ten.
The answer is simple.
These go to eleven.

Nigel Tufnel's (Christopher Guest) response to filmmaker Marty DiBergi (Rob Reiner) inquiry about his band Spinal Tap's amp. While other bands' amps' dials are metred from zero to ten, Spinal Tap's go from zero to eleven. Although most people would associate "going up to 11" purely with Spinal Tap, Fender Champ amps from the early 1950s actually had volume controls that went up to eleven (1).

Nigel: "You see, most blokes will be playing at 10. You're on 10, all the way up, all the way up...Where can you go from there? Nowhere. What we do, is if we need that extra push over the cliff: eleven. One louder."
DiBergi: "Why don't you just make 10 louder and make 10 be the top number, and make that a little louder?"
Nigel (after taking a moment to let this sink in): "These go to 11." (1)

Because of This Is Spinal Tap's tremendous influence on pop culture, the phrase "up to eleven" is now listed in the "Shorter" edition of the Oxford English Dictionary (meaning "at maximum volume") (2). Irony of listing in the short version and not the long version notwithstanding, the vernacular phrase has also come to mean "being at the utmost level of excellence" among metalheads.

Referencese:
1: http://spinaltapfan.com/atozed/TAP00160.HTM
2: http://www.timesonline.co.uk/printFriendly/0%2C%2C1-3564-427663%2C00.html