I am looking for a simple explanation of what burning "fees" means and implies in the context of EIP-1559.
In EIP-1559, burning the Base Fee means that the Base Fee is not sent to anyone. The Base Fee vanishes rather than being sent to the miner/validator.
In the specification it looks like:
# miner only receives the priority fee; note that the base fee is not given to anyone (it is burned)
self.account(block.author).balance += gas_used * priority_fee_per_gas