The Chromatic Scale

The chromatic scale is a musical scale with twelve pitches, each a semitone above or below another. On a modern piano or other equal-tempered instrument, all the semitones are the same size (100 cents). In other words, the notes of an equal-tempered chromatic scale are equally spaced.

All 12 notes of a chromatic scale makes up an octave(a tone on the eighth degree from a given tone.)
As you probably noticed, you add a sharp(#) when ascending in a scale and a flat(b) when descending.

To help you understand what an octave is just play an open string and then the 12th fret on the same  string. You'll hear the same tone but at a higher pitch.