twig = suddenly realize something. With emphasis on sudden. understand = means to know something in depth. It could be known for a long time.

To 'understand' is the widely used norm throughout the various types of English, whereas 'twig' is a purely British and informal usage. I hope this helps.

In U.S. English, a "twig" is a small and slender tree branch, so it's interesting to see that it has this alternate meaning in British English.