A fundamental frequency is the lowest frequency generated by any given note on an instrument. Harmonic frequencies are frequencies generated by various aspects.
A sine wave is also known as a pure tone and produces no harmonic frequencies. On a frequency spectrum, you will see a single frequency being generated by a sine wave. A triangle wave is similar to a sine wave with a slight more rigid shape. This will produce the first few harmonics.
A sawtooth wave is a further deviation from the triangle wave and will produce harmonic frequencies all the way up the spectrum.
A square wave is unique in that it only produces odd harmonics and has a distinct characteristic.
In terms of frequency in Hertz, harmonics are integer multiples of the fundamental frequency.
Consider a frequency of 100Hz. Its harmonics would be represented at 200Hz, 300Hz, 400Hz, 500Hz and so on.
A frequency of 500Hz would have harmonics at 1kHz, 1.5kHz, 2kHz, 2.5kHz, 3kHz and so on.
Octaves are achieved by doubling the fundamental frequency.
For instance, if I press the note middle C on a synthesizer, it will generate a signal at 524Hz. If I press C an octave higher it will generate a signal at 1048Hz. Conversely, if I press a note an octave below middle C, it will generate a signal at 262Hz.
Understanding the Hz scale will greatly benefit the music production process as a whole.