ERC20 tokens are deployed with functionality that allows other smart contracts, for example, atomic swap contracts, to move tokens. By approving the smart contracts, it now has permission to execute the peer to peer swapping behavior.
The Allowance Permission is the total amount of tokens that are able to move in the swaps. By default we set the allowance to a high value, so you don't have to approve your tokens every time you want to trade.
Below is an example of what this approval looks like in MetaMask: