1. understand, usually after some initial difficulty
e.g. She didn't know what her classmates were plotting but finally caught on
Synonym: catch onget wiseget ontotumblecotton ontwigget it
2. adopt
e.g. take up new ideas
Synonym: take upfasten onhook onseize on
3. take hold of or attach to
e.g. The biochip latches onto the genes