Here "the blood" refers to the death of Jesus. Just as Moses sprinkled blood on the people of Israel to symbolize their covenant with God, believers are in covenant with God because of Jesus's death.
This passage speaks of grace as if it were an object that believers could possess, and of peace as if it were something that could increase in amount. Of course, grace is in reality the kind way God acts toward believers, and peace is how believers live in safety and joy with God.