In the case of Arjuna, performing one’s duty according to Dharma means serving as a warrior should (“kṣatriya dharma”).
This means being willing to go into battle, even if one will fight one’s own kin (as in the case of the Pāṇḍavas fighting the Kauravas).
In prioritizing Arjuna’s dharmic duty over personal worldly concerns (such as worries about battling one’s kin), Kṛṣṇa thus articulates a model of behavior for renouncing the ego on the yogic path to mokṣa (as negating the ego eliminates karmic bondage to saṃsāra).