The interval whose frequency ratio is 2/1 or 1200 cents (¢).
The Diapason in Greek.
An 8ve is often not exactly 2:1, but merely somewhere in the vicinity. The name comes from the Latin word for 'eight', and is due to the fact that in the diatonic major scale that was long standard in European music, the 8th degree was the one bounding or approximating the 2:1 ratio with the fundamental.
A physical length of key-span on the keyboard, covering 8 white keys. Here is an illustration of one octave of the standard halberstadt keyboard, labeled from A to A:
