Something very loud, brash or overly exuberant. As in "turned up to eleventy stupid".
This is a reference to This Is Spinal Tap, in which the lead guitarist Nigel Tufnel proudly shows off his custom amplifier. The dials on the amp go up to 11, whereas most amps go up to ten. Nigel is under the impression that this makes it "one louder". This line is quoted in many other media, including the volume control on the BBC iPlayer.