Being pedantic, but it's beyond that.

To grok is to know or understand so completely, it becomes a part of yourself. To know something fully. You can understand the concepts of astrophysics, but you might not grok the concept.

Specifically, it refers to a deep understanding.

[A critic] notes that [the coiner's] first intensional definition is simply "to drink", but that this is only a metaphor "much as English 'I see' often means the same as 'I understand'". (from Wikipedia)

When you claim to "grok" some knowledge or technique, you are asserting that you have not merely learned it in a detached instrumental way but that it has become part of you, part of your identity. For example, to say that you "know" Lisp is simply to assert that you can code in it if necessary – but to say you "grok" Lisp is to claim that you have deeply entered the world-view and spirit of the language, with the implication that it has transformed your view of programming. Contrast zen, which is a similar supernatural understanding experienced as a single brief flash. (The Jargon File; also quoted on Wikipedia)

For those who aren't familiar with the word, it comes from the 1961 scifi novel "Stranger in a Strange Land".