Cross-chain atomic swaps enable trustless exchange between different cryptocurrencies by allowing users to swap one cryptocurrency for another directly on separate blockchains without the need for a trusted intermediary. This is achieved by using smart contracts that ensure that either both parties involved in the swap receive the agreed-upon amount of the other cryptocurrency, or the swap is canceled and neither party loses their funds. This eliminates the need for trust in a centralized exchange or third party, as the swap is entirely automated and self-executing based on predetermined conditions.