Grok is a verb roughly meaning "to understand something so thouroughly that you have become one with it or even love it" (Koster 28).
It was first coined by Robert Heinlein in his novel Stranger in a Strange Land, but Raph Koster makes use of it in his book A Theory of Fun for Game Design in order to describe the level of understanding a player can reach after playing a game so many times that it becomes second nature. It is similar to the concept of muscle memory.