Atomic Swaps is the ability to swap or perform transactions between bitcoin and any other cryptocurrency.
Atomic Swaps can be used to make transactions across network of various blockchains(chains) without trusting third party janitor or intervention.
A Cross-Chain Atomic Swapping is one the amazing and emerging features of Lightning Network as it allows a Participants says in Litecoin chain to instantly, trustless and securely swap his funds with another Partcipant completely on another different chain eg Bitcoin.
Since The Transactions takes place within Lightning Network, The transaction fees will be very liitle or even negligible. This Atomic swapping is really good as users privacy is stilled maintained across the Network.
Atomic Swapping is 100% possible as long as both chain(Eg Bitcoin, Litcoin etc.) can support the same cryptographic hash function. With this in place, the Peers or Participants can easily send funds or perform trustless transactions between different blockchains.