Here's a breakdown of the meaning:
* Tongues: Refers to people's speech and gossip.
* Wagging: Implies a rapid, active, and often malicious spreading of rumors or criticisms.
Example: "After the celebrity couple announced their separation, tongues were wagging about who was to blame."
Other ways to say "tongues were wagging":
* People were talking behind their backs.
* The rumor mill was churning.
* There was a lot of speculation.
* There was a lot of chatter.
* People were spreading gossip.