Basically a github maintainer can add their project to commiteth so that whenever someone posts an issue with a label "bounty" a bot posts an address. That address is an ethereum smart contract. People all around can send ETH to that address in order to add incentive to the fix. In Ethereum, contracts can have balances just like wallets.
When a pull request comes in that says it fixes that issue, the bot sees that. Through the smart contract it authorizes the package maintainer to disburse the funds to the fixer at the maintainer's discretion.