The expression is an American expression that originated during World War II, and means beware of unguarded talk (See here.)
This idiom is also apropo at the poker table.
Friday I played in a satellite to enter the main event and saw this hand:
Player A raised fairly big from late position and the big blind called. The flop was all low cards with two diamonds. It was checked to Player A and he bet 2000 and the big blind called. The turn was a third diamond and the big blind bet 2000 into Player A.
"Let's keep it rolling," he said as he looked at Player A and smiled.
Player A folded his aces face up and the big blind showed him ♦A ♦3 for the nut flush.
Perhaps he would have gotten more chips from the A-A hand if he had kept quiet, but we'll never know. It was an easy laydown with his talk.