Climbers use grades to tell each other how difficult a climb is - that way, one can choose a climb of appropriate difficulty. Grading systems are complex; there are different ones in every country and for every type of climbing.
In the U.S., rock climbing is graded with an open-ended scale that begins at 5.0 and currently extends to 5.15. (The 5 refers to 5th class, or climbing with ropes and protection; lower classes range from walking to scrambling). Each grade from 5.10 up is subdivided from "a" to "d." You might see, for example, 5.10b or 5.12c. Frequently the 5 prefix is left off (e.g., 10b).
When a climb is first ascended, the climber grades the route based on her experience with climbs of similar difficulty. As more people do the climb, a consensus on the grade will be reached. Most people begin rock climbing at 5.4 to 5.7. With a few years of experience, they may feel comfortable on 5.9 to 5.11 climbing. 5.12 and up is the terrain of experts.