latch_on
1. [ verb ] adopt, as of ideas
Synonyms: take_up seize_on hook_on fasten_on
Related terms: espouse
2. [ verb ] understand, usually after some initial difficulty
Synonyms: get_it catch_on get_onto twig cotton_on get_wise tumble
Examples:

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

Related terms: get_the_picture