As a supplement to Siren's nifty node above, here is what I know about climbing grades (the Yosemite Decimal System, YDS, used in the United States) and what they mean in terms of subjective difficulty.

The YDS system rates climbs on a scale of 5.1 to 5.15. The scale originated as an extension of a US geological grading system that classified terrain on a scale from 1 (flat land) to 5 (graded or vertical with ropes and harnesses recommended for safety.) Climbers (since they almost always used ropes and harnesses) extended this system by creating a scale from 5.1 to 5.10, with 5.10 being physically impossible for a human to climb without direct aid from ropes and harnesses (as opposed to just protection.) Eventually, the impossible 5.10 was reached and surpassed, and the scale was extended over time as climbers found themselves ascending more and more difficult routes. Here's a breakdown of the rating system:

  • 5.1 - 5.3 : These are the very easiest routes to ascend. 5.1 corresponds roughly to a steep pile of rocks. 5.3 could be anything from a steep, featureless, but walk-able grade to a vertical wall with "jug handle" placements. (I seem to recall there being a ladder at my climbing wall that was rated a 5.3 . . . )
  • 5.4 - 5.5: A slightly less easy route. Typically vertical with large hand and foot placements available; usually an average sized person will be able to stand at rest at any point on the wall and reach the next hand or foot-hold with out straining or reaching too far. Its fair to say that a healthy young person with a little nerve should be able to climb a 5.4 or even a 5.5 on their first day out with no problem.
  • 5.6 - 5.7: Slighly harder these ones are. The hands and foot-holds may require some significant reaching or even a dyno to accomplish, or it may require one or more tricky matches. Usually it takes the novice a few tries to get these climbs, but sometimes particularly tall or gifted folks can do these right away.
  • 5.8 - 5.9: These are intermediate difficulty climbs. Usually the holds are smaller or less easy to grasp/stand upon, requiring the climber to support him or herself on only a small part of the foot, or use only the first two segments of the digits of the hand. In general these climbs require a bit of poise and confidence, thus it takes practice to be able to climb at this level.
  • 5.10 - 13: Advanced climbs. These routes typically feature very small holds, challenging overhangs, and heavy use of smearing (using only the friction on the wall to support yourself.) It is at this level that you may encounter climbs that are physically difficult to do because of limitations in height of arm span. At the higher levels, the holds may be nothing more than pockets in the wall able to hold one or two digits.
  • 5.14: The hardest of climbs. Very few 5.14's exist in comparison to all other rated routes, and very few people can climb them, (I have met one person in my life who claims to be able to do 5.14.) These climbs might be all pockets, or might require climbers to hold onto the wall using little more than one good foot-hold and the friction on their fingers. If you can do these regularly, consider yourself a professional.

The table in siren's WU above is considered to be current, with 5.14c/d being the hardest do-able climbs. No 5.15 climb exists today, and it is now considered to be the theoretical limit for human performance. Chris Sharma, a young hot-shot from the Santa Cruz area supposedly attempted route considered to be the first 5.15 (consisting of two 5.14c routes wedded together.) I haven't been able to find out how he did . . .

Keep in mind though that with this system YMMV. You might find that the large, hip, for-profit indoor climbing facility will sandbag their routes - i.e. boost the rating to make their clients feel like they are climbing higher than their real ability. Or you might find a club populated with particularly skilled climbers that concentrate on routes rated 5.11 and above and will set 5.6 - 5.9 rated routes that are unusually hard.

Finally, real live rock is VERY different from an indoor sport wall. The weather can be intimidating (e.g. sun glare, high heat), the routes can take you much higher than even the most elaborate walls, and the rock can crumble and slip out from your fingers depending on the conditions. If you've only ever done indoor climbing before, you can bet that on your first day out on a real rock you will climb at least one decimal below ability.