Auto-battle is a great mechanic that allows you to skip battles with weak neutral units while still gaining experience, unit resurrection, etc. It works simply: when you attack any enemy, the auto-battle results are shown immediately, and then you can either accept them or play the match yourself. This really saves time and eliminates monotonous battles where you just shoot down tier 1-2 units. 

The setting is enabled in the general game settings and is accessible both from the main menu and during the game. 

Many think that after this, auto-battle will be automatic and the results cannot be replayed, but that is not the case. 

The battle results can be replayed. If auto-battle triggered, you will see a "To battle" button in the results.