Burning coin is performed in the early stages of a new cryptocurrency in order to avoid that early users hold the largest portion of supply in the market, so that they won't be able to manipulate the market itself or that the coin is a scam. If you hold the largest share of supplies you can control its price fluctuation and this is not good for the health of the currency since that would mean that the market could be rigged, causing users to flee from the market. Burning your coins is a way to show your commitment to the currency on the long term and to earn trust from the users that want to join the market.

My understanding is of the following:

Who does it? - In a lot of scenarios, the founding company themselves generally hold on to a large supply of coins to either burn, release at a later stage or 'lock up'.

Why? - By burning their own coins their value per coin will increase and this will increase interest in potential buyers and current coin holders.

However the above case is a common case, but not always the way coins are burned. Sending the coins to non existent address or sending the coins to an address without a private key can technically result in a 'burn'.