Grok is a term originating in Robert Heinlein's Stranger in a Strange Land. In it Mike (the main character) is from Mars, raised in an entirely different culture from anything like that of earth, a key element of which is water. The importance of water is apparent throughout Martian culture and understanding how relevant water is to survival, particularly in an environment which lacks much of this key building block of life. From this understanding we may also "grok in fullness" other ideas from Mars such as: water brotherhood (which is accomplished by sharing a glass of water with another, though it does not have to actually be physical water for the person to become your water brother), to the importance of water-sharing which stems from water brotherhood to the literal meaning of grok (to drink).
When one drinks water what happens is that the liquid is taken into the person's very physical being, and from that the essences of the two substances mingle together and become one. This is a very roundabout way of saying what grok means: understanding, knowing, feeling, being a part of, "mini-enlightenment"; all of these things rolled into one are what to grok is. Another point is the cerishing which goes into this newly groked object. You can draw from your own experince to understand this cerishment: Ever had a really big day of yardwork in the sun, and looking forward to a nice big glass of ice water, feeling the water flow through you. That, in a sense, is part of what groking truly is.
The reason that understanding how the word "grok" came about within the Martian culture is very important because one of the central themes within the book is an adaptation to culture, and therefore one should look at the culture Mike was raised in, the very core of which in its beginnings was to acquire water and therefore survive, and as the civilization advanced a main driving force of it was to "drink" all things it came across.
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