to explain something to someone; to imply something to someone. (Possibly misleading someone, accidentally or intentionally. See also given to understand.) Mr. Smith gave Sally to understand that she should be home by midnight. The mayor gave the citizens to understand that there would be no tax increase. He didn't promise, though.

[of someone] made to believe [something]. (See also someone to understand">give someone to understand.) They were given to understand that there would be no tax increase, but after the election taxes went up. She was given to understand that she had to be home by midnight.