What is a major innovation from the fish to the amphibian/reptilian circulatory system?

A double circulation. With the onset of a three chambered heart amphibians could now send blood to the lungs to pick up oxygen from a new environment, the air. As evolution progressed toward reptile development, the beginnings of a 4th heart chamber appeared allowing the animals to become more active and along with changes in reproduction (amniote egg) and a thicker less vascular skin the reptiles moved away from a water environment.