Śrīla Nārada Muni is giving a practical example from his past life. Formerly, during the previous lifetime of Lord Brahmā, Nārada Muni was one of the denizens of Gandharvaloka, but unfortunately, as will be explained, he fell from his exalted position in Gandharvaloka, where the inhabitants are extremely beautiful and expert in singing, to become a śūdra. Nonetheless, because of his association with devotees, he became more fortunate than he was in Gandharvaloka. Even though cursed by the prajāpatis to become a śūdra, in his next life he became the son of Lord Brahmā.
The word mahā-kalpe is described by Śrīla Madhvācārya as atīta-brahma-kalpe. Brahmā dies at the end of a life of many millions of years. The day of Brahmā is described in Bhagavad-gītā (8.17):
ahar yad brahmaṇo viduḥ
te ’ho-rātra-vido janāḥ
“By human calculation, a thousand ages taken together is the duration of Brahmā’s one day. And such also is the duration of his night.” Bhagavān Śrī Kṛṣṇa can remember incidents from millions of years ago. Similarly, His pure devotee like Nārada Muni can also remember incidents from a past life millions and millions of years ago.