One way to look at octaves is that they are the skeleton for any tuning.
Above, is for the tone A. We will explore all of the octaves, using A. We also will explore each octave at its origin. Origin means however it is played at the nut.
All of the other tones orbit these shapes.
There are 7 octaves that our hands can reach comfortably. And, a double octave .
If we explored each octave, thoroughly, wouldn't we know our whole board?
7 things is a pretty good number.
Fact: there are 7 octave shapes on the guitar in standard tuning for 6 string guitars [not including double octaves that can be fretted]. They are the ultimate skeleton [the bare bones; frame to fill in; wrapper for any chord, scale, and/or arppegio] to understand the layout of the fretboard for any tuning. Octaves are a very effective way to see how the tones on the guitar are organized. We will base our studies on understanding each of the 7 octaves.
These shapes are consistent for every tone. Our example shown on the skeleton is for the tone A. And, we are labeling the root zero, rather than one [Numera; see tone naming]. The 'origin' - the chord forms - are within the grid showing all of the octave shapes on one fretboard, and labeled for each octave along the side of the break outs.
Once we know the octave shapes for any given tone, they are same for every other tone, and they always cycle in the same order.
An octave is an interval of an 8th, such as C to C, or A to A. It is a frequency doubling or halving of a tone (twice as fast or slow).
In Western music, scales are typically heptatonic (7 tones). Therefore, the completion of a scale, whether Major or minor or other, is the 8th, which is the same letter name, or tone, as the first. (Oct- means eight). Within an octave are 13 tones (13th completing), and 12 half steps.
In cultures using Pentatonic scales (5 tone scales) as their primary melodic & harmonic tone material, the 'octave' could be called a 6th, rather than an 8th. In 12 tone music (dodecaphonic), the 'octave' could be called a 13th.