An octave is a 2:1 frequency relationship. If one A vibrates at 440 Hz, the A an octave above vibrates at 880 Hz; the A below vibrates at 220 Hz.
In the equal-tempered system used here, the octave contains twelve semitones. On a guitar, moving up twelve frets halves the vibrating string length approximately and raises the pitch by an octave.
A standard 88-key piano spans seven octaves plus a minor third, from A0 to C8. It covers a wide range, but not the entire range of musical or audible sound.
Pick up your guitar
Find C on more than one string. Notice that the same note name can occur at different pitches an octave apart.