Modern Warfare is a sort-of a spin off of Call of Duty. It is within the franchise but has its own system of sequels. So this isn’t the 3rd installment in the Call of Duty series–it’s the third installment of the spin off.
Call of Duty: Modern Warfare 3 is First-person Shooter rooted in a fictional, but ultra realistic near-future conflict of mostly American forces with those of the Russian Federation around the globe. The third installment in the Modern Warfare branch of the Call of Duty franchise, Modern Warfare 3 features a heavy focus on multiplayer gameplay which includes innovative new functionality that encourages multiple gameplay combat strategies, a new 2-player co-op option, new play modes, weapons and more. The game also includes a gripping single player campaign that picks up where Call of Duty: Modern Warfare 2 left off, and game integration with the Call of Duty: Elite online service.
I haven’t played any of the Modern Warfare games yet myself, but some of my friends really like this series. Please note, the comments on Amazon complain that the map system in Modern Warfare 3 is not up to the quality of previous editions.