A store is your own smart contract the the NEAR blockchain. This is the same concept on our Ethereum side as well. Each store name is a subdomain of our NFT smart contract factory, currently mintbase1.near so a store name of soul4Space would be soul4Space.mintbase1.near.
Think of it as your own company and deploying a store is a set of unchanging functions that lives not on ours or your servers, but on the blockchain. You can deploy and manage as many stores as you want. You do not have to use the mintbase UI to interact with it.
Every action on your store is free for anyone to see and can be observed on the NEAR block explorer (mint, sell, burn, transfer). Anyone can create a block explorer as all of this data is public and unchangeable.