Hosts burn coins by sending them to a provably unspendable address. Hosts are expected to burn a portion of their revenue (~4%) as a demonstration that they are real. Renters will select hosts that have burned coins with a probability that grows in a linear relationship to the total number of coins burned. Therefore, a host that has burned 2x as many coins will be twice as likely to be selected as another host that has all other factors the same. This provides a very important defence against Sybil attacks. An attacker that is trying to manipulate a renter will need to have all of the excess redundancy of a file before being able to commit an attack. For a file with 3x redundancy, that means the attacker will need to get at least 2.1x of that redundancy, which means that the attacker will need to burn enough coins to look like 67% of the network. That entails burning 1.5x as many coins as the rest of the network has burned combined. Especially as the network grows and matures, collecting that many coins is going to be prohibitive. (Source)