Octave
Definition
The musical interval between a note and another with exactly double (or half) its frequency — they sound like the ‘same’ note, higher or lower.
Technical definition
A 2:1 frequency ratio. The human ear perceives pitches an octave apart as equivalent (octave equivalence), which is why note names repeat every octave across instruments and cultures.
Example
Middle C is about 261.6 Hz; the C above it is 523.3 Hz — one octave higher, double the frequency.
Common confusion
An octave is a ratio (2:1), not a fixed number of hertz. Going from 100 to 200 Hz is an octave, and so is 1000 to 2000 Hz — the absolute difference changes but the ratio does not.