Motion control shoes are the most rigid, control-oriented running shoes. They're designed to slow down or limit extreme inward rolling of the foot and ankle, which can cause injury (this excessive rolling is called 'overpronation').
Motion control shoes are generally heavy but very durable. They may include features such as a medial post (a firmer section under the inner edge of your foot, for pronation control); a polyurethane midsole (for midsole durability) and a carbon rubber outsole (for outsole durability). Many are built on a straight last, which offers stability and maximum support on the inner side of your foot.
You should buy these if: you’re an overpronator who needs control features and places a premium on durability; or you wear orthoses (sculpted shoe inserts) and want a firm midsole and deep heel counter; or you’re a heavy runner who needs extra durability and control. Runners with flat feet often do best in motion control shoes. Choosing a Shoe: The Very Basics | Interactive Shoe Finder