Dyneema is a Ultra High Molecular Weight Polyethylene (UHMWPE) which offers strength without sacrificing weight. Up to 15 times stronger than steel(weight for weight), Dyneema is used in the airline, mining, energy, commercial fishing industries as well as the military. The application for a lightweight & strong fiber is limitless.
In shoes, the Dyneema fiber is woven into the fabric of the upper to provide extra stregnth(at no real weight cost to the consumer). Allowing shoe manufacturers to target "no stretch zones" in tennis shoes and apply Dyneema to prevent unwanted stretching of the shoe. This provides extra stability and durability. The material is also extremely breathable, water resistant and UV resistant.
For more on Dyneema, visit their website: here.