In plain words
He brought many kings' daughters, many women and young girls, held them captive and tormented them in many ways in his prison. Unable to bear these sufferings, many cried out to Kṛṣṇa. They begged Him to slay the demon who had arisen to wipe out mankind itself, to rescue their lives and to bring about the welfare of mankind. Death must come through the very ones who were tormented. Whoever kills with the sword meets death by the sword. For a man who lives by evil qualities, those very evil qualities torment him. In the same way, the wicked one of this day had tormented women in many ways; so his death had to be brought about by women. To that end He was to take Satyabhāmā along and slay that Narakāsura. The day on which he was slain is this Naraka Caturdaśī. This is the day people have called Naraka Caturdaśī. The second day is the Amāvāsyā. Kṛṣṇa set free from bondage the sixteen thousand maidens who were in bondage to that Narakāsura. Kṛṣṇa commanded them to go back, each to her own home. But these sixteen thousand Gopīs too fell at Kṛṣṇa's feet and prayed. 'Svāmī, because we have been in this prison all this time, in the power of this wicked one, every single person in society suspects us. Society does not respect us. Rather than live a life with such disrespect, it is far better to be dedicated at Your feet,' they said.
'You who have saved our lives in so many ways, can You not maintain us? So protect us, cherish us and maintain us,' they asked. 'You who bear the whole world, can You not bear us?' they prayed; and at that He gave His promise: 'I will protect these sixteen thousand Gopīs, I will bear them.' Because He bore these sixteen thousand Gopīs, He came by the name Bhartā. You cannot say that Bhartā means 'husband', the man a woman marries. Bhartā, because he is the one who bears. Bhāryā means: because she is the one who is borne. So, because we could not grasp the meaning of these words, people have gone on saying, by way of slander, that Kṛṣṇa even married sixteen thousand Gopīs. These sixteen thousand Gopīs were wholly dedicated souls. Because He uplifted their lives, cherished them and bore them, Kṛṣṇa came by the name Bhartā.
So this Amāvāsyā day is the day He bore the Gopīs. The Caturdaśī day is the day Narakāsura was killed. This Amāvāsyā day is full of darkness. It is black dark. 'He is the One who lit the lamp of our lives in such darkness': so they prayed that from today life should be, all of it, a full-moon night. That is why, though today is only the darkness of the Amāvāsyā, wherever you look people have lit these sparklers, lit lamps in many ways, and spent this whole night today like a full-moon night.