The leaffer replaced its ancestor the lumbering ketter. Its ancestor was so big and slow that predators easily picked them off. Those born with legs like their distant ancestors survived. In addition those also born with more leaves than normal survived and within a short time they grew many leaves on their backs.
Not all of their ancestors adaptions were phased out; some were improved upon. For instance rather than having their entire legs as a water carrying device they grow bubbles on the sides of their legs to store water in. This allowed them to both store up water and move. Their skin is not as thick as their ancestors were but this allows for more flexibility when running from predators. In addition with so many more leaves absorbing sunlight it has much more energy and thus can stay more active. They can go longer between drinking and can even regulate their body heat better.
Their reproduction has also evolved. They will still mate by kissing. They will grow wooden seed-eggs rather than zygote balls. When the seed-eggs have developed enough they are spit out and then buried near by fresh water. Once they hatch the tiny offspring will have food and water nearby to consume until they are large enough to leave their oasis homes.