To evolve is to change from one form to another, radically different form. The obvious example would be Darwinian evolution... However, you can apply this more generally. For example: "Even though he was a bad student way back when, but he's really evolved into an excellent professional," or, per random Google search, "...Social Media Will Evolve Into Social Business."
To develop means rather to grow slowly, adding piece by piece or layer by layer to what's already there. You develop a skill, for instance... a basketball player is said to develop his jump shot, while somebody working abroad develops an accent. An infant in the womb is developing. Development need not always be positive however: somebody can develop a bad habit, while "recent developments" in the news often point to a turn for the worse.
So, in summary, "to evolve" means to dramatically change into something entirely different, while "to develop" means to gradually change into something different.