Rock and Mountaineering
2nd Class: Trail hiking/walking
3rd Class: Difficult hiking. Easy, unroped scrambling. Use of hands may be required.
4th Class: Moderate to difficult scrambling. Careful attention required for feet and hand placements. Rope may be prudent.
5th Class: Vertical climbing. Rope is definitely required. Class 5 routes are further broken down:

5.0 - 5.2: Extremely easy roped climbing (tenured climbers would not likely rope up).
5.3 - 5.5: Easy climbing (anyone new to climbing typically starts here without any problems).
5.6 - 5.7: Moderate climbing
5.8 - 5.9: Difficult climbing
5.10 - 5.11: Very challenging
5.12 - 5.13: Extreme! (full time climbers)
5.14: Currently the most difficult

Water Ice (WI) and Alpine Ice (AI)
WI1: Extremely low angle ice. With crampons, one could simply walk.
WI2: A steep walk. Mountaineering axe or Ice tool may be helpful.
WI3: Sections of steep/vertical ice can occur. Crampons and ice tools are required.
WI4: Continuous sections of vertical ice are encountered. Rests are harder to come by.
WI5: Vertical ice. Placing protection requires hanging from your ice tools or rope.
WI6: Over-hanging, thin, or rotten ice. Placing protection is very hard.

AI ratings basically parallel WI ratings except that Apline Ice is usually no more than hard-packed or densified snow.

Mixed Climbing
Mixed climbing involves "dry tooling" on rock in an effort to connect with small patches of ice. The "M" rating system starts at M1 and continues to...M12??? (someone keeps climbing a harder one). The difficulty of any mixed route can change in an hours time. Ice may melt or break off making the climb easier or more difficult, depending on the new condition. It is said that M6 is roughly equivalent to 5.10 rock climbing in terms of the physical/techinical skills required.