ayam avatāro rajasopapluta-kaivalyopaśikṣaṇārthaḥ.
ayam avatāraḥ—this incarnation (Lord Ṛṣabhadeva); rajasā—by the mode of passion; upapluta—overwhelmed; kaivalya-upaśikṣaṇa-arthaḥ—to teach people the path of liberation.
In this age of Kali, people are overwhelmed by the modes of passion and ignorance. Lord Ṛṣabhadeva incarnated Himself to deliver them from the clutches of māyā.
The symptoms of Kali-yuga are predicted in the Twelfth Canto, Third Chapter, of Śrīmad-Bhāgavatam. Lāvaṇyaṁ keśa-dhāraṇam. It is predicted how fallen souls will behave. They will keep their hair long and consider themselves very beautiful, or they will pluck out their hair as the Jains do. They will keep themselves unclean and will not wash their mouths. Jains refer to Lord Ṛṣabhadeva as their original preceptor. If such people are serious followers of Ṛṣabhadeva, they must also take His instructions. In the Fifth Chapter of this canto, Ṛṣabhadeva gave His one hundred sons instructions whereby they could become free from the clutches of māyā. If one actually follows Ṛṣabhadeva, he will certainly be delivered from the clutches of māyā and return home, back to Godhead. If one strictly follows the instructions of Ṛṣabhadeva given in the Fifth Chapter, he will certainly be liberated. Lord Ṛṣabhadeva incarnated specifically to deliver these fallen souls.
Link to this page: https://prabhupadabooks.com/sb/5/6/12