Rotary encoders, in the most recognisable form, are mechanical devices that look a bit like potentiometers, and are often used in their place. Some audio gear uses them, and are recognisable as volume controls with regular bumps or clicks as they turn. They are also used in mechanical trackballs and mice, as well as lots of other applications that require accurate rotational sensing.
In hobbyist applications, they are handy for all sorts of things - potentiometer replacements, up/down switching, etc. Using them with AVRs, PICs and Arduinos is quite common and they are easily available.
