The coop is where they sleep at night and lay eggs. The run is where they spend most of their day just being chickens. The bigger the chicken breed, the bigger the coop and run need to be. The more chickens you have, the more room you need. A run will be needed if you don't want them destroying your landscaping. Nothing in your yard will be safe from them otherwise. They especially like to scratch around in flower beds and can render beautiful lawns into dust and dirt in a matter of weeks.
X2 on junebuggena; also whether or not your let them roam free in the yard will depend on the predator situation where you live. In a coop/run (if it is built properly) your flock will be protected from predators, whereas free ranging in a yard, they are much more vulnerable to predators. There is a good article at http://www.the-chicken-chick.com/2013/07/11-tips-for-predator-proofing-chickens.html on predator proofing your chickens. Also, unless the fence around your yard is 8 ft. or more, you will need to clip the flight feathers on one wing of each chicken to keep them from flying over the fence.