This means if I want to trade you my magikarp for your full art Zekrom both cards must be marked as "Copies I want to trade:" regardless of who is creating the trade.
What happens if the cards are not marked is you can click accept but it will just return to the offers window without accepting the trade.
Note that you do not have to recreate the trade to get it accepted. Both people in the trade can just mark their cards "Copies I want to trade:" then the trade can be accepted.
I hope this helps.