To mouth something means to form words with your lips and tongue without actually making sound, or to say something in an insincere way that you don't really mean.

When you mouth words silently across a classroom to a friend, you're shaping each word with your mouth so they can read your lips, but no sound comes out. Actors sometimes mouth their lines silently while rehearsing. During a loud concert, you might see someone mouthing “I'll be right back” because shouting wouldn't work.

The word takes on a different meaning when someone mouths platitudes or mouths empty promises. Here it suggests saying the right words without any real feeling or intention behind them. A politician might mouth support for a cause while doing nothing to actually help it. When someone just mouths off, they're speaking rudely or disrespectfully, often without thinking first.

The past tense mouthed works for both meanings: “She mouthed 'good luck' from across the auditorium” or “He mouthed the same excuses he always did, and nobody believed him anymore.”