transitive verb. To understand profoundly through intuition or empathy.

verb. To have or to have acquired an intuitive understanding of; to know (something) without having to think (such as knowing the number of objects in a collection without needing to count them: see subitize).

verb. To fully and completely understand something in all its details and intricacies.

verb. get the meaning of something

"For those of you who read Robert Heinlein, you will realize that I stole the term grok from his novel, Strangers In A Strange Land, which was practically required reading for hippies."

understand  

catch on  cotton on  digest  figure  get it  

grokked  grokking