"Now take this one word: 'grok.' Its literal meaning, one which I suspect goes back to the origin of the Martian race as thinking, speaking creatures—and which throws light on their whole 'map'—is quite easy. 'Grok' means 'to drink.' "
"Huh?" said Jubal. "But Mike never says 'grok' when he's just talking about drinking. He—"
"Just a moment." Mahmoud spoke to Mike in Martian.
Mike looked faintly surprised and said, " 'Grok' is drink," and dropped the matter.
"But Mike would also have agreed," Mahmoud went on, "if I had named a hundred other English words, words which represent what we think of as different concepts, even pairs of antithetical concepts. And 'grok' means all of these, depending on how you use it. It means 'fear,' it means 'love,' it means 'hate'—proper hate, for by the Martian 'map' you cannot possibly hate anything unless you grok it completely, understand it so thoroughly that you merge with it and it merges with you—then and only then can you hate it. By hating yourself. But this also implies, by necessity, that you love it, too, and cherish it and would not have it otherwise. Then you can hate—and (I think) that Martian hate is an emotion so black that the nearest human equivalent could only be called a mild distaste."
Mahmoud screwed up his face. "It means 'identically equal' in the mathematical sense. The human cliché, 'This hurts me worse than it does you' has a Martian flavor to it, if only a trace. The Martians seem to know instinctively what we learned painfully from modern physics, that the observer interacts with the observed through the process of observation. 'Grok' means to understand so thoroughly that the observer becomes a part of the process being observed—to merge, to blend, to intermarry, to lose personal identity in group experience. It means almost everything that we mean by religion, philosophy, and science—and it means as little to us as color means to a blind man."
He takes it too far, though. A word so broad as to cover "almost everything that we mean by religion, philosophy, and science" isn't going to be very useful. Maybe that's why, to the extent the word survived the novel, its meaning narrowed.
It's broad in the human (as opposed to Heinlein's Martian) sense because we engage with religion, philosophy, and science in a largely intellectual way. Yes, even wingnut fundamentalists. They're all highly linguistic things; most of our more mystical traditions have fallen by the wayside for one reason or another.
In the Martian sense, that mystical perspective is far more useful: it unifies their physical reality of transcendent Old Ones and life that can be grown through singing and so on. The presence of a single word signals that they've collapsed all of these things down to a simple concept; the lack of a human analog simply says we haven't.
So to make a long thing short, the word cuts to the heart of a conceptual area that we can but dance around with all of our words and qualifications and half-understandings in the fields of religion, philosophy, and science. The desire to know divinity, to know oneself, to know the universe: these can be streamlined into a single concept, to grok.
Thus why Heinlein goes on to have Mike explain his pantheistic "God is that which groks". The closest English word I know of is not "understand" but rather "suffuse" or "permeate". To me, the reason the word survives the novel as a mere stronger version of "understand" is because most people hand-waved the novel's walk-through of religion as a boisterous critique rather than as a considered and valid approach to life, the universe, and everything.
I played amateur philosopher as a teenager and I actually spent a good 5 pages or so on a paper trying to describe this concept... and I think my result had less precision. This is before I had read Stranger.
The quotes at http://en.wikipedia.org/wiki/Grok imply that in Heinlein's novel, to grok something meant to merge one's being with it in a kind of total rapport. So, something more than a variant of cognitive understanding. I haven't read the novel though.
In Stranger in a Strange Land grok was the Martian word for "water".
But water was so tied up to everything in their culture that what it really meant was virtually anything. In particular it meant to really "get" what something meant, or what someone else was saying.
