What does 'like knows like' mean?

In general, it's meaning is simple and intuitive - the more similar a person is to oneself, the easier it is to get to know or understand that person.

A second but related meaning of the phrase is knowing through analogy. This usage goes back at least to the Presocratics, especially Empedocles.

Though it might seem to be used as a substitute for the phrase, "it takes one to know one", "like is known by like" is not normally used pejoratively like the former is. Another difference is that "it takes one to know one" does not seem to allow for degrees of likeness/knowledge.

The concept of "like is known by like" was a major philosophical doctrine at least as early as the 5th century B.C.E. Pythagoras taught that the extent or depth of our knowledge of the divine depends on us being like the divine, or assimilating to the divine. The idea was that to the degree that we have knowledge of the divine, we must have changed our own character from human to divine.

The doctrine of "like is known by like" was quite influential on later philosophical and religious schools of thought, especially Neoplatonism.

One might also apply the phrase in ethics without referring to other minds (divine or otherwise), to mean "being good enables or helps one to know the good". The idea that virtue somehow illuminates moral truth suggests that more virtuous people have a greater ability to know moral truth.