What is the difference between Optical Fiber Single Mode and Optical Fiber Multi mode? and which applications are used for every mode?

http://www.multicominc.com/training/technical-resources/single-mode-vs-multi-mode-fiber-optic-cable/

have look at the link I hope that you will find all your answer.

Multi mode fiber has a relatively large light carrying core, usually.5 microns or larger in diameter. It is usually used for short distance transmissions with LED based fiber optic equipment. Single-mode fiber has a small light carrying core of8 to microns in diameter. It is normally used for long distance transmissions with laser diode based fiber optic transmission equipment.