Αὐτοὶ ἐνίκησαν [Autoi enikēsan] , they, they overcame . Emphasis is placed upon the redeemed who overcame Satan by Gods work. They are among the true overcomers (Rev. Rev. 2:7+, Rev. 2:11+, Rev. 2:17+, Rev. 2:26+; Rev. 3:5+, Rev. 3:12+, Rev. 3:21+; Rev. 17:14+; Rev. 21:7+). See Who is the Overcomer?
by the blood of the Lamb
Satan is able to accuse the brethren continually because the brethren continually sin (1Jn. 1Jn. 1:8). Thankfully, the one-time sacrifice of the Lamb of God justifies them eternally. Satans accusations toward the believer are essentially made against the perfect righteousness of Christ. This is how they overcame him by the blood of the Lamb. In our initial appeal to Christ for salvation, His work on the cross takes into account all our sin, both past, present, and future . Our sin only affects our fellowship with Him, not our standing as a justified one (1Jn. 1Jn. 1:9). Once we come to faith, Satan now appeals to the Judge Who is also the Justifier (Rom. Rom. 8:33). Concerning the blood, see the commentary on Revelation 1:5. Concerning the Lamb, see the commentary on Revelation 5:6.
The rest of her offspring have the testimony of Jesus Christ (Rev. Rev. 12:17+).
they did not love their lives
They did not love is οὐκ ἠγάπησαν [ouk ēgapēsan] , which speaks of love, especially of love as based on evaluation and choice, a matter of will and action.1 Ἀγαπάω [Agapaō] speaks not so much about altruism, but intensity. Jesus said the Pharisees love (ἀγαπάω [agapaō] ) the best seats in the synagogue (Luke Luke 11:43). John wrote that men loved (ἀγαπάω [agapaō] darkness (John John 3:19).2 Lives is ψυχήν [psychēn] , also translated souls (see below). Among these are the ones who had been beheaded for their witness to Jesus and for the word of God, who had not worshiped the beast or his image, and had not received his mark on their foreheads or on their hands (Rev. Rev. 20:4+). These are they of whom the world was not worthy (Heb. Heb. 11:38), which include the martyrs of the fifth seal (Rev. Rev. 6:9+) and many coming out of the Great Tribulation who were martyred for their faith (Rev. Rev. 7:14+; Rev. 15:2+).
to the death
Ἄχρι θανάτου [Achri thanatou] , until death , the same phrase Jesus used when writing to the persecuted church at Smyrna (Rev. Rev. 2:10+). These overcomers followed His instructions and maintained their testimony to the point of death and obtained the crown of life (Rev. Rev. 2:10+). Their death was merely a gateway to the continuance of their eternal lifetheir souls were safe. They did not fear those who could only kill the body: And do not fear those who kill the body but cannot kill the soul (ψυχην [psychēn] ). But rather fear Him who is able to destroy both soul (ψυχην [psychēn] ) and body in hell (Mtt. Mat. 10:28).