Defination of Single mode and Multimode
First of all we need to know the word mode ,mode here means the travelling patch of the light wave in the fiberglass. Single mode cable means this cable is suitable for light wave to travel in the cable in one mode, while multimode means this cable allow light wave to travel in the cable in multiple mode. below are the two pictures illustrating how the light travel in the single mode fiber and multimode fiber.

Light travel in single mode fiber:

Light travel in multi mode fiber:

Brief illustration of structure of Single mode cable and Multimode cable for fiber patch cord
the structure of the cables used on fiber optic patch cords are like this : fiberglass in the center, with cladding around the fiberglass, the most outside part of the cable is called jacket. below is a picture for illustration of the structure.

Difference between single mode fiber cable and multimode fiber cable:
single mode fiber cable is known as 9/125 fiber optic cable, here 9 means 9um, it is the diameter of the fiber core.125 means 125um ,it is the diameter of the cable cladding. usually multimode cables are 50/125 ones and 62.5/125 ones. for multimode fiberglass, you can imagine it is similar as size of the human hair ,so we can know a single mode fiber glass is even smaller size. actually ,it is 8.3um not 9um, but it is the custom practice people call single mode cable to be 9/125 type cable.
judging from the jacket colors ,this is an easy way to tell the difference. Single mode fiber optic cables are with bright yellow color jacket ,while multimode fiber optic cables are with orange color jacket.
Usually when we get a piece of indoor fiber optic cable, for example, a fiber optic patch cord or fiber optic jumper, we can also see on the cables there are words printed on them ,besides words such as 9/125,50/125 or 62.5/125, there are also words like SMF-28 as you can see on some Corning fiber optic cables, here SMF is just short for Single Mode Fiber. Also there may be names of the manufacturer of this fiber optic cable ,and production date, etc printed on the cable.