Characteristics
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.
Types
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.
Falls
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.
Treatment
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.