The Dolphins already picked up their future quarterback in the first round (Ryan Tannehill) so they move to defense in the second round.
SB Nation's NFL draft blog, Mocking The Draft, explains the pick:
Branch would fit the role as an outside pass rusher for the Dolphins. Cameron Wake is one of the best pass rushers in the league, but he needs someone to lessen the attention he receives. It's a similar thing to what the Redskins did by adding Ryan Kerrigan across from Brian Orakpo. A college defensive end, some question whether Branch can covert to linebacker. But there were the same questions last year about Kerrigan and he was excellent. Branch has some experience dropping in coverage, both with his hand down and from a linebacker stance.