What is an octave?

An octave is a note that sounds the same as another note to the human ear, the only difference is it being higher or lower. It's hard to explain what it is without hearing it, so pick up your guitar and play any string. Then fret that string on the 12th fret and play it again. The second sound will be much higher, but it will seem to have the same sound. Exactly what it is takes a little music theory, so here is the skinny

Looking at a piano illustrates this-

as you can see, I've highlighted in red all the notes that there are. There are only 12 notes. Then the piano repeats itself. (that's also why 12 frets up is the next octave) Same with all music, there are only twelve, then everything repeats itself in octaves.

*You might hear it called a diapason or perfect 8th as well, but only by the more musically literate.