I believe it means we resort to the truth of what the shedding of blood points to: The work of the cross. The blood is simply a concept that speaks, using few words, about all the truths of the cross. So, really, it is simply saying I stand on the work of the cross of Jesus in dying, being buried and resurrecting to save my soul for whatever need in my life that I am pleading for.
It is simply using the reference to the BLOOD the way the bible did use it as follows:
Hebrews 10:19 KJV Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus,