Grok (pronounced GROCK) is a verb from Robert A. Heinlein's science fiction novel, Stranger in a Strange Land (1961). In it a Martian visits earth and brings his language from Mars. Grok means to understand, in an utterly complete and intuitive way. It's the Martian equivalent of to "get it", and the youth culture adopted this new word into the English language.
Example usage: "Many politicians cannot grok the facts: conservative principles are good for our nation, good for our youth, and good for ourselves."
Grok is probably the only English word that comes from the language of Mars.