To grok (pronounced GRAHK) something is to understand something so well that it is fully absorbed into oneself. In Robert Heinlein's science-fiction novel of 1961, Stranger in a Strange Land, the word is Martian and literally means "to drink" but metaphorically means "to take it all in," to understand fully, or to "be at one with." Today, grok sometimes is used to include acceptance as well as comprehension - to "dig" or appreciate as well as to know.
As one character from Heinlein's novel says:
'Grok' means to understand so thoroughly that the observer becomes a part of the observed - to merge, blend, intermarry, lose identity in group experience. It means almost everything that we mean by religion, philosophy, and science - and it means as little to us (because we are from Earth) as color means to a blind man.
In common usage, "Do you grok?" seems close in meaning to "Do you get it?"