In couple words:
There is a big difference in the diameter of the core, the actual path of the light. Singlemode fiber has much smaller core that only allows a single mode (or a single light ray or wave) to propagate. This allows for less dispersion of the signal and, therefore, higher data rates and greater distances. The downsize of the singlemode fiber is the fact that, due to the small size of the core, big portion of the light's energy is lost before the light even enters the fiber. This leads to higher energy light sources that are more expensive themselves and require more complex and expensive control circuitry.
Multimode fiber on the other hand, has much greater core diameter, which allows for better coupling of the light energy. That makes it possible to use cheaper light sources. The downsize is: it is prone to signal dispersion. This limits both speed and distance at which multimode fiber can be deployed.
Dmitri Abaimov, RCDD