To understand something so completely that it becomes a part of oneself.
From Robert A. Heinlein's 1961 science fiction novel, "Stranger in a Strange Land."
Richard Feynman, the late physicist, had an expression, "If you can't explain it simply, you don't understand it well enough." To grok something is to have incorporated the concept so firmly in your mind that it becomes more than a tool, it becomes an extension of you. I try to learn something every day and to grok something until not only does it make sense to me, but to the point of owning it, whether a programming concept, a literary term, a historical event, or more.