"Multimode fiber is like shooting a shotgun down a conduit - you get a lot of pellets into it, but they tend to bounce of the walls so they don't go very far and they aren't very accurate.
Singlemode fiber is like firing a rifle down the conduit - it's just a single bullet but it will go straighter, faster, and further than the pellets. "
- Jim Jachette
This is the explanation that made sense to me. Both modes are one shot of light.
As for why the two modes exist.
Singlemode equipment use to be very expensive. Multimode equipment was alot cheaper than Singlemode. So it made sense to use multimode on the short distances.
Today the equipment prices and fiber prices themselves are almost equal. People are just hung up on multimode or need to maintain existing multimode networks.
If you are building a new fiber network, just go for Singlemode.
Hope this helps.