The more you know

[Donald Trump]

From NBCs public service advertisements. During the short clip a celebrity personality will state some fact, followed by the ending The More You Know sequence.

Can be used as a sarcastic response to learning some typically useless knowledge, trivia or fact.

[Tina]

A reference to NBC public service announcements which would feature celebrities reciting a random (usually touching) fact, followed by the statement, The More You Know.
Thus, a person may say this after reciting something that is not necessarily useful to the listener. It may also indicate that the user does not expect a response from the listener.
Often rendered like a tag, e.g. #themoreyouknow.