Burning coins is the process of reducing the total number of coins in circulation.  Dependent on the coin this can be done in many ways. Typically, when coins are transfered, there is a Tx fee which is often burned.

Burning coins slows inflation. POS does increase supply and burning reduces supply. i.e. if you combine or split blocks a fee is charged which burns coins.

With coins, there is a balancing act between POS, POW (also increases # of coins), burn, initial supply, time, & demand.Coins can also be burned in swaps designed to reduce supply and hopefully increase price per coin.