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Quick reminder about octaves.
In music, an Octave is the interval between one musical pitch and another with double its frequency.
Here is an example on the A note:
Visually in this picture above we can see that A1 and A2 are octaves. They both have an A note. That means essentially it is the same note right?
Well yes, it is in fact the same note. Just in a different pitch.
So if you are playing a note and some one tells you play “An octave above” Or “An octave below” they are telling you to play that same note just a region above or below.
In the video example below you can hear it sounds the same. The first note played is A1 which is in a lower pitch than the second note being played which is it’s octave A2.
In this sense, you are playing an octave above A1.
More of an explanation.
This happens to a note when a note is doubled in frequency.
A1 has the frequency of 55.00
A2 has the frequency of 110.00
and when A2 is doubled in frequency, we get to its octave.
A3 has the frequency of 220.00
A4 has the frequency of 440.00
As we can see the pattern now, this will apply to the upcoming A octaves.
A5 has the frequency of 880.00.
A6 has the frequency of 1760.00
And ETC.
I hope this helps elaborate on the why to octaves 
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