We have been enjoying this in our gatherings lately! "They (we) overcame him by the blood of the Lamb" means that all our standing is in Christ. This is the only thing that shuts the Accuser's mouth. None of our lowly righteousness is worthy, and is powerless against the devil. We, instead of looking to our own merits or devices, are to look away unto Jesus. He is the Brass Serpent held up for us to behold, and thereby be healed. The devil's accusations cannot continue, because God is fully satisfied with the perfect sacrifice of His Son.
When we then proclaim His blood, the devil is put to flight. This is the Christian's foundation for everything, and apart from Him we can do exactly nothing.
So His blood, and our speaking/testimony of it is our only foundation. Then, comes the part about not loving our life (Gk. psyche - soul life) unto death. The Accuser is put to flight, and then we put off the old man and put on the new man (which is Christ in us). This is a matter of obedience to Him in spirit, but the foundation is always His inputted righteousness paid for with His own blood.
(I didn't give any references here, as I felt I was replying to someone established well enough in the word to follow. But if needed, please just ask.)
REPLY TO JEREMY 8/27: Yes, I see how you might want more of a scholarly answer. And before I answer, allow me to say this: I was never a bible scholar by any means, but I have done my fair share of reading scripture, commentaries, and looking into the Greek. Plus I have many around me who have religious degrees, read Greek well, teach others, etc. that I fellowship with on a continual basis. All of that certainly has value, and I appreciate those near me who the Lord has blessed with this function for the body. But in the end, all of that amounts to exactly nothing without revelation. As He says, "Apart from Me you can do nothing." Zero; zip; zilch; nada. (Jn 15:5) And Paul says clearly that knowledge will fail and only love remains. (1 Cor. 13:8)
To illustrate, please read the comment I made today to the moderator, James. I would trade all the studying and head knowledge for a single, brief flash of revelation light from the Spirit. To be sure, the Spirit speaks the same as the logos (written word), but even the Pharisees had the logos - yet didn't know Christ at all when he was there with them. Even though they were steeped in scriptural knowledge, they needed light from above to see who He was. So I do value reading the bible daily, but without the experience of Light, it is like the negative sitting in a camera just waiting to be exposed. (Another example of this is when I first came to know the Lord, He showed me many things instantly in spirit, that it would take years for me to mentally comprehend - like, "I is dead" . Now I see in the logos the words that support those revelations, e.g., Gal 2:20.)
So back to your excellent question. Someone else (Steve Taylor) already pointed out that this verse says they "overcame him by the blood . . ." This shows that this overcoming is because of His blood. His blood is mentioned first for a reason. Without His shed blood there is nothing. First is His blood, then we witness His His blood by speaking the fact of it. The result is they loved not their soul-life (Gk "psyche") unto death.
This verse really encapsulates the Christian life. Christ came, died, and shed His blood completely apart from our involvement. We give nothing for this and it is not earned - it is simply a fact. "While we were yet sinners, Christ died for us." (Romans 5:8) Our portion in this - our work - is simply to believe on Him. (Jn 6:29) When we believe in His death and resurrection and declare this, we are saved. (Rom. 10:9)
Now that the Grain of wheat fell into the ground to give His life to us, we are the many grains sharing this same life. (Jn. 12:24) With Christ in us (Col. 1:27) as the Spirit (2 Cor. 6:17), we share His death and resurrection (Gal. 2:20). Therefore, with this hope of glory (what is to come), we "put off the old man" (who we were formerly) and "put on the new man" (Eph 4:22-24), thereby not loving our "soul-lives unto death."
"AND THEY OVERCAME HIM BY THE BLOOD OF THE LAMB AND BY THE WORD OF THEIR TESTIMONY - AND THEY LOVED NOT THEIR SOUL-LIVES UNTO DEATH." WOW! What a passage is in Revelation 12:11 - summing up the whole Christian life!!! Thanks for asking me to explain this a little deeper. What a Christ we have!