He is the son of Maharṣi Jamadagni and Śrīmatī Reṇukā. Thus he is also known as Reṇukāsuta. He is one of the powerful incarnations of God, and he killed the kṣatriya community as a whole twenty-one times. With the blood of the kṣatriyas he pleased the souls of his forefathers. Later on he underwent severe penances at the Mahendra Parvata. After taking the whole earth from the kṣatriyas, he gave it in charity to Kaśyapa Muni. Paraśurāma instructed the Dhanur-veda, or the science of fighting, to Droṇācārya because he happened to be a brāhmaṇa. He was present during the coronation of Mahārāja Yudhiṣṭhira, and he celebrated the function along with other great ṛṣis.
Paraśurāma is so old that he met both Rāma and Kṛṣṇa at different times. He fought with Rāma, but he accepted Kṛṣṇa as the Supreme Personality of Godhead. He also praised Arjuna when he saw him with Kṛṣṇa. When Bhīṣma refused to marry Ambā, who wanted him to become her husband, Ambā met Paraśurāma, and by her request only, he asked Bhīṣmadeva to accept her as his wife. Bhīṣma refused to obey his order, although he was one of the spiritual masters of Bhīṣmadeva. Paraśurāma fought with Bhīṣmadeva when Bhīṣma neglected his warning. Both of them fought very severely, and at last Paraśurāma was pleased with Bhīṣma and gave him the benediction of becoming the greatest fighter in the world.
Ref >> Srila Prabhupada Vani.