To make it easier to understand we can compare it to how torrent clients work. In order to have your shop where to sell your items, you will have to host your shop on some device so that other users can interact with your store and see listings, same as how on the torrent client you receive files from another user. For the beginning, you can use devices like raspberry pi as it should be good enough to handle the load of buyers on the marketplace. When people buy and sell between each other they do it directly without any middleman. For data storage, OpenBazaar uses IPFS, a protocol and a network designed to be a distributed file system. Though it is possible if your store is cached with IPFS that you do not have to keep your store online 24/7 to enable customers to buy whenever they want to.
One of the advantages of OpenBazaar is that the payment process is bitcoin plus as everything is peer to peer there are no fees on the platform itself. Of course, if you are looking to sell items you will have to cover the cost of running your own shop or hosting it somewhere on the internet.
By default, IP addresses of anybody who use OpenBazaar are available. If you, however, seek for greater privacy running it through Tor is also made possible.
OpenBazaar implements some sort of traditional escrow system. Where there is some 3rd party, middleman, a man in the middle between buyer and seller. By using moderated payment when a buyer wants to buy an item he sends the money to a multisignature, multisig, address. Multisig enables multiple parties to be required in order to spend the funds and in this case, it requires at least 2 parties, out of 3 involved, to agree on how they want to release the payment. By doing this seller will get the money only after the buyer is satisfied or seller will get the refunds if there is some problem with an item he or she bought no matter the reason. Anybody can become Moderators and thus help to solve issues on the OpenBazaar that buyers and sellers may have.