Course of a Tournament:

Arena begins running the tournament always with the pairing with the lowest number of games. If in all pairings the same number of games are played, Arena continues with the pairing that is on top of the list.

So from all pairings the first game is played (round 1). Then the second game of all pairings (round 2), etc.. One round is one column in the list of pairings.

You can raise the number of rounds safely, e.g. in order to continue a tournament.

Also it is not a problem if you insert an engine into a tournament that has already started. If in the current tournament e.g. 2 rounds are played, Arena continues with the pairing with the lowest number of games. These are the pairings of the newly inserted engine, because this engine hasn't played any. The next round (here the third) will be started, when all pairings have the same number of games.