A round is an instance of a stage. Each time a proof enters a new stage, it also enters a new round.
Information on activities that take place and events that occur is saved in the round information, ensuring that a complete history is kept and made available as necessary to authorized users.
In the capture of the round diagram above, we can see that a file went from the Copyread approval stage back to the Production stage (presumably to fix a text error). From the Production stage, the file went to the Customer approval stage, and from there it was sent to the Finished stage.