Token burning is the process of permanently removing tokens from circulation. This is usually done by sending them to a special address that no one holds the keys to, often called a burn address, so the tokens can never be moved or used again.
Projects burn tokens for different reasons. Reducing the total supply is a common one, sometimes described as a way to affect scarcity. Some protocols burn a portion of fees automatically as part of how they are designed, while others do occasional one-off burns.
It is important not to read too much into a burn on its own. Reducing supply does not automatically raise a token value, since price depends on many factors including demand. This entry explains what burning is; it is not a suggestion that a burn makes any token a good or bad choice.