Question

why do you rub a matchstick on the side of the match box to burn it

Answer 1

The tip of the matchstick contains phosphorus which has a low ignition temperature(the temp at which it starts burning). So when the phosphorus is rubbed against the box due to friction heat is released which increases the temperature and so the phosphorus on reaching its ignition point starts burning.

Answer 2

When we rub a matchstick on the side of the matchbox, friction is generated which in turn burns.