The docs are fairly technical and assume you already know how atomic swaps work. We'll add an high-level overview. That is very good feedback! We are doing atomic swaps for far too long so we sometimes assume everyone knows...

Apart from that the concept always consists of two steps as Michael explained further down: first lock coins then claim them atomically. For the chain part of the swap that always means two transactions.

For chain -> LN swaps transaction cost is X (estimated based on current mempool high priority fee) because user wallet already pays for the lock transaction. For LN -> chain swap transaction cost is ~X*2 because user needs to pay for both lock & claim transaction.