If you put something about , you tell it to people that you meet and cause it to become well-known. ( The forms put around and put round are also used in British English. mainly BRIT )
Moderates are putting it about that people shouldn’t take the things said at the Republican Convention too seriously...
The King had been putting about lurid rumours for months.
PHRASAL VERB : V it P that , V P n (not pron) , also V n P