Diodes are commonly used discrete semiconductor device. It has many uses and purposes. Its operation is based on PN semiconductor junction characteristics. Depending on diode physical and chemical properties it can behave very differently. Together with other electronics components diode can be used for voltage clipping, multiplying, rectifying, signal, demodulation, protection and even more. Elektro-labs have written pretty nice review of diode types and their common uses.
Simplest and probably most recognizable is regular diode which is used in switching, protection rectification circuits. Another common diode type is Zener which is used for voltage stabilization, then list goes on LEDs and photo-diodes and finishes with more exotic ones – tunneling diodes and varactors.