The greatest difference is between the core diameters: 8.3 micrometers for singlemode versus 62.5 (or 50) micrometers for multimode. If I try to greatly simplify things, I would say that the small diameter makes it possible for only one mode (or path of light or ray, though rays are imaginary) to travel through the core of a singlemode fiber. Thus there is no difference in the time of arrival between the modes (dispersion), and the signal can be sent at much greater frequencies and travel much greater distance. On the other hand, larger core of a multimode fiber makes it possible to collect more light energy from weaker and less precise sources, like LEDs, that makes it more affordable and easy to install.
Dmitri Abaimov, RCDD