The friction created when you strike a match triggers a series of chemical reactions, causing it to ignite and then combust. To produce a flame, you need something to burn (fuel), oxygen and enough heat. The match head contains sulphur, glass powder and an oxidising agent. Meanwhile, the striking surface is made of sand, powdered glass and red phosphorus.
The heat generated when you strike the match converts some of the red phosphorus into unstable white phosphorus, which spontaneously ignites. This starts a chemical reaction, allowing the oxidising agent to produce oxygen. The presence of heat and oxygen allow the sulphur to combust, creating a flame.