It's a tool to sell items to other players for Energy Credits. You can sell every item that is not bound to your character.
So if you have a valuable item that is in demand but not really usefull to yourself you can post it there with an offer how much credits you want for it. Other players can then see the offer and decide to buy it. If no one buys it, the item will be returned to you.
I would suggest to look what the current best price is for the item and undercut that for your own offer.
Keep in mind that it might not be worth to sell on the exchange if the best price is not significantly more then half the designated in game value. In that case just sell to a vendor.
If you are unable to raise the funds for the excelsior in time by yourself feel free to ask me or Trek for fleet help. We can then help you out.