Relayers are like postmen in the real world. They are watching EVM-based chains, and when they see a Mayan Swap transaction, they fetch VAAs of the transaction from Wormhole guardians and then commit those signed VAAs on the Solana network. This requires spending Sol tokens. So relayer should be incentivized to perform on behalf of users; that's why users have to pay relayer fees.
Relayers have no access to users' funds and the Solana program is trustless, so anyone can run its own relayer to transfer the signed messages.