John Wimber, founder of the Vineyard Church, coined that phrase. He used it to illustrate that Christians are to display their supernatural abilities in very natural ways. For instance, praying for the sick, and believing that God can and does heal people.
I think there is more to it than that. I believe there to be no such thing as the dichotomy between natural and supernatural. We divide the two because we are influenced by Greek philosophy, and because we want to distinguish between what we believe to be an inconsistency between science and faith.
The problem is that God did not set up two worlds or realms; He works in one. He created the universe therefore He set it up to run as, what is from our perspective, both supernatural and natural. But there is no dichotomy--there is no separation. Our universe is at one and the same time both natural and supernatural with no distinguishing between the two.
This is another area where our eschatology (our understanding of the end of things) has interfered with our theology. We constantly view things in terms of the "end of it all." So, we create this other realm that is supernatural. So for God to do something he "interferes" with the natural order of things. Miracles were seen as God's changing the normal course of things. So, when science or liberal theologians proposed natural explanations for things, conservatives had to back track.
But the supernatural is a natural part of our world.
Miracles are simply God's action in His world. The blooming of a flower is simply miraculous in God's world.