EtherMium is a decentralized exchange for ERC20 tokens (native Ethereum blockchain tokens).
An exchange is a place where buyers and sellers meet to exchange assets for other assets. The exchange is meant to connect buyers and sellers safely while protecting the identities of traders from each other. An exchange is also expected to provide a space where liquidity can be concentrated (instead of traders searching for each other, they can meet in the same place to perform trades).
A traditional centralized exchange would act as a third party providing the place to trade, custody of users funds and order matching between traders. This conventional approach requires all user funds to be kept in a secured location by the exchange acting as a custodian. This approach creates a host of security issues due to the tempting nature of a big pot of money just sitting somewhere. Hackers, software bugs, government seizures are just several examples of risks inherently present in centralized exchanges.
A decentralized exchange is meant to overcome those security risks by not giving access to the funds to any third party and leaving the funds in possession of the user at all times. This is achieved by creating a smart contract on the Ethereum blockchain that is responsible for holding user funds. The contract is designed so the creator of the contract cannot control the funds inside (to read in more detail how this is achieved, check this article). The user always has control of the funds, no third party, hacker or government can access them while all users are anonymous.