Atomic swaps provide a way for two cryptocurrencies to be exchanged using a single blockchain and without a trusted third party involved.
In computer lingo, "atomic" means something that either happens fully, or does not happen at all.
An "atomic swap", is a cryptocurrency swap operation that either completes successfully, or everything is rolled back and funds are returned to both parties.
An atomic swap can be implemented using a smart contract.
This contract would be activated by either participating party in the swap. This user would deposit their part of the deal and the smart contract will start a countdown clock.
If the other party does not deposit their part of the deal within a predetermined period, the deal is cancelled and the initially deposited funds are returned.
On the other hand, if the counterpart does deposit their share, the contract executes the swap and both parties receive their funds.
All of this happens without the intervention of a trusted 3rd party - which is what makes the system different from a typical brokered transaction.