Full Frame is just another term for 35mm sized sensor. In other words the actual sensor in the camera is the same size as a single frame of 35mm film.
Cropped sensors are those normally found in P&S cameras, or in consumer grade DSLR's. Big full frame sensors are expensive, so the they make smaller sensors for low-end cameras. The term cropped is just describing smaller field of view on the smaller sensor cameras.
As far as lenses.....gonna half to be more specific about which type of lenses.
Unless you are talking about the difference between full frame lenses and digital lenses.
The full frame lenses have the optics tuned for a wider field of view, so they take full advantage of the larger sensor size.
The digital lenses have the optics tuned for a smaller field of view for the smaller sensors.
For instance. Nikon labels their digital lenses with the abbreviation "DX" indicating that they are tuned for cropped sensor size cameras, and "FX" for full sized/film lenses.
You can however put full frame lenses on cropped sensor cameras, and vise versa. But there is a conversion factor that takes place.