"Every day, Krsna and Balarama used to go in the forest and some asura would come to disturb Them, to kill Them, and Krsna will finish them. And the friends will come at home and narrate the story to their mothers, "Mother, Krsna is so wonderful. Such a big demon came and He killed immediately in this way and that way." That is Krsna."
Srila Prabhupada Lecture on Srimad-Bhagavatam, 09-28-72, Los Angeles
"So here Krsna Caitanya and Nityananda, Their identification is Lord Krsna and Balarama. Now, in the Krsna incarnation, these two brothers were engaged as cowherd boys and friends of the gopis, sons of mother Yasoda and Nanda Maharaja. That is actual life in Vrndavana. Krsna and Balarama, They are village cowherds boy. That is the early age history of Krsna-Balarama. And Their another business, when They went to Mathura They killed Kamsa and the wrestlers, and then again, when They went to Dvaraka, They had to fight with so many demons. But Their childhood life, up to sixteenth year, They were in Vrndavana, happy life, simply love. That is paritranaya sadhunam. Sadhus, devotees, they are always anxious to see Krsna, Balarama and Their associates. They are always very much aggrieved on account of separation. To give them rejuvenation of life, Krsna-Balarama play Their childhood days in Vrndavana. And out of Vrndavana, beginning from Mathura up to Dvaraka and other places, the business was vinasaya ca duskrtam: killing. So They have got two businesses, one for pacifying the devotees, and the other is to kill the demons. Of course, Krsna and Balarama, They are Absolute Truth. There is no difference between killing and loving. They... Absolute. Those who were killed, you know, they were also delivered from this material bondage."
Srila Prabhupada Lecture on Caitanya-caritamrta, 03-26-75, Mayapur
"Thus Krsna has no work to perform. As the Supreme personality of Godhead, He simply engages in enjoying Himself with the gopis (cowherd girls) and His consort Radharani. Krsna, as Krsna, does not really engage in killing demons. When Krsna kills demons, He is known as Vasudeva Krsna, not the original Krsna. When Krsna expands Himself, He first expands as Balarama, then Sankarsana, Pradyumna, Aniruddha and Vasudeva. As Vasudeva, He acts in Mathura and Dvaraka, but as Krsna, in His original feature, He remains in Vrndavana. This may seem to be confusing; even one of the greatest fiction writers in Bengal misunderstood and thought that Krsna of Vrndavana, Krsna of Dvaraka, and Krsna of Mathura were three different persons. But this is not difficult to understand if we know the nature of Krsna's expansions. Krsna is the same, and He is the one without a second, but He can expand Himself in billions and trillions of forms. This is all for the purpose of His enjoyment."
Elevation to Krsna Consciousness, Chapter 5
Bhaktivedanta Book Trust. Excerpted from texts and purports of HDG A.C. Bhaktivedanta Swami Srila Prabhupada.