These settings control the sampling quality of the rendered images. Increasing the sampling rates reduces the amount of noise in the images, but at the expense of increased rendering time.
You will notice that this evolution is not linear, as, for each of these sampling rates, the actual number of samples is the square of the input value. For example, if Camera (AA) samples is 3, it means that 3x3 = 9 samples will be used for Anti-Aliasing. If Diffuse samples is 2, then 2x2 = 4 samples will be used for the GI. The same applies to the other values.
Diffuse, Specular, Transmission, SSS, and Volume sampling rates are expressed for each Camera (AA) sample. This AA sampling rate can, therefore, be considered as a global multiplier for all the other ones. In this example, the total amount of Diffuse samples per-pixel is, therefore, 9x4 = 36.
The different per-pixel sample counts are listed at the top of the section.
Further information about sampling can be found here.
Sampling is divided into the following sections:
More information about working with sampling and removing noise can be found here.