From https://code.google.com/archive/p/fractalterraingeneration/wikis/Fractional_Brownian_Motion.wiki
Octaves are how many layers you are putting together. If you start with big features, the number of octaves determines how detailed the map will look.
The frequency of a layer is how many points fit into the space you've created. So for the mountain scale, you only need a few points, but at the rock scale you may need hundreds of points. In the code above, I start with a small frequency (which equates to large features) and move to higher frequencies which produce smaller details.
The amplitude is how tall the features should be. Frequency determines the width of features, amplitude determines the height. Each octave the amplitude shrinks, meaning small features are also short. This doesn't have to be the case, but for this case it makes pleasing maps.
Lacunarity is what makes the frequency grow. Each octave the frequency is multiplied by the lacunarity. I use a lacunarity of 2.0, however values of 1.8715 or 2.1042 can help to reduce artifacts in some algorithms. A lacunarity of 2.0 means that the frequency doubles each octave, so if the first octave had 3 points the second would have 6, then 12, then 24, etc. This is used almost exclusively, partly because octaves in music double in frequency. Other values are perfectly acceptable, but the results will vary.
Gain, also called persistence, is what makes the amplitude shrink (or not shrink). Each octave the amplitude is multiplied by the gain. I use a gain of 0.65. If it is higher then the amplitude will barely shrink, and maps get crazy. Too low and the details become miniscule, and the map looks washed out. However, most use 1/lacunarity. Since the standard for lacunarity is 2.0, the standard for the gain is 0.5. Noise that has a gain of 0.5 and a lacunarity of 2.0 is referred to as 1/f noise, and is the industry standard.