It’s pretty simple, really. We believe that God loves to heal people, so we pray, often, for Him to do what He loves to do.
More than that, we believe that it’s God who heals, not the people praying. That means that it’s not something reserved for super-Christians, but is actually something that all of us can play a part in. You should try it sometime.
Here’s a cool video from one of the Vineyard Movements crazy young leaders, Robby Dawkins, talking about healing prayer. http://vimeo.com/30889060.