twig

nouns

a small branch or division of a branch (especially a terminal division); usually applied to branches of the current or preceding year

branchlet, sprig, twig

is derived from

branch out in a twiglike manner

"The lightning bolt twigged in several directions"

twig

is a type of (narrower)

divide into two or more branches so as to form a fork

"The road forks"

understand, usually after some initial difficulty

"She didn't know what her classmates were plotting but finally caught on"

catch on, cotton on, get it, get onto, get wise, latch on, tumble, twig