twig

(noun) a small branch or division of a branch (especially a terminal division); usually applied to branches of the current or preceding year. Synonyms: branchlet, sprig.

(verb) branch out in a twiglike manner. Example: "The lightning bolt twigged in several directions."

(verb) understand, usually after some initial difficulty. Synonyms: catch on, get wise, get onto, tumble, latch on, cotton on, get it. Example: "She didn't know what her classmates were plotting but finally caught on."