Side Encounters are the battles you are not required to win in order to progress further in the game. They become available as the storyline unfolds.
You can tackle Side Encounters multiple times, and they become harder each time you return to the one completed earlier; just hold on for a bit until the Encounter resets. Side Encounters are available only alongside Main Encounters, and you can have more than one available to try at the same time.

You will get Experience, Silver and Items as a reward.

Auto Battle mode is available for Side Encounters from level 4, and you will need Auto Battle Tickets to use it. You need to turn this feature on before the battle kicks off.