Ropes used for climbing can be either dynamic or static; the two are used for different applications, and while a dynamic rope can be used in applications where static ropes are better, static ropes can't be used in place of dynamic ropes.
Dynamic ropes are designed to stretch upon impact, so that when a climber falls, much of the force is absorbed by the rope instead of the climber's body.
Dynamic ropes can be used as either single lines or double ropes; single ropes are 9mm to 11mm in diameter; double ropes, which must be used as a pair, are 8mm to 9mm.
Ropes are rated for how many falls they can absorb before breaking; the test used to determine a fall rating is much more severe than any actual climbing fall, but ropes should still be retired after holding any long falls.
Ropes can be treated with a chemical that helps to repel water; such ropes are called dry ropes, and are preferred for ice climbing and mountaineering.
Dynamic vs. Static
Static ropes don't stretch when put on a load; this makes them very good for hauling equipment up a climb, or used as a fixed line that a climber will ascend with Jumars.