As explained elsewhere, this is a rough guide to the sort of stars you will be able to observe with your equipment. Again, as a ball-park value, 'bright' means that the whole of the variation cycle can be followed with a small telescope; 'medium' stars can be followed with (for instance) telescopes up to and including about 12" aperture, while faint stars need larger instruments to cover most of their variations.
These guides are based, wherever possible, on practical observing. For example, V1057 Cygni has a range of between 10th and 16th magnitude, but for many years it is expected to hover around magnitude 13, and so appears as a 'medium aperture' star. It was first noticed when it rose from the sixteenth magnitude in the 1970's, which is where the magnitude 16 minimum originally comes from!