It's nor too difficult a concept, but I'll try explain. Similar to the lenses in glasses, they're moulded a certain shape from materials with known light-bending properties. The shape and material determine how magnified the image that gets to your eye is.
The material doesn't need to be thick ,it just needs to have a high refractive index and a suitable difference in curvature between the front and back faces of the lens. Incidentally, most contact lenses wearers are myopic (i.e. short-sighted), so their lenses don't magnify, they diminish. That is to say, if you are short-sighted, without correction you will see things bigger than they actually should be, but out of focus.
I had been in the optical trade for 20 years and the video was extremely interesting to me as I only worked in the manufacturing side of glass and plastic lenses so I thank-you `mibn2cweus for that. I am now retired, thank God.