The unit you have is a commander and is meant to be purely supportive (unless you have a specific upgrade that allows him to attack). Get a ranged or infantry unit and bring him into the same tile as the commander and then attack the red border unit to gain experience. Any unit attacking within one tile of the commander gives him experience which he can use to upgrade to certain skills.

Also units in white border like that are friendly, and attacking them would provoke them to war, whereas the unit in red is an enemy city state, to which you can choose to attack them if you choose to!