Miroslav Bodecek, leader and editor of Tezos Domain posted an introductory article on medium explaining how they plan to run the Name system.
Blockchain Name service helps solve the problems of long complicated addresses, take for example a Tezos wallet address. One can not easily read or memorize the Alphanumeric patterns of wallet addresses and this applies to all cryptocurrency wallet addresses out there. The Naming system solves this problem by attaching human readable wallet addresses to those standard addresses. An example to quickly understand the system is: say you wanted to replace a standard wallet address like tz52VS….kcjb with an easy readable form like this Sam.tez . This simple form will allow users to easily read and memorize wallet addresses and might not copy paste your address the next time they need to send you some Tezos. It also helps Developers to attach names to their smart contracts making it easier for Dapps to discover and interact with those contracts. Miroslav pointed out that this is only an early draft and is likely to be changed along the way. You can see the proposal here.
Further Info
The project plans to sell names at open action, bidding will be public and names sold to the highest bidder. Domain names that are expired or had no buyers previously will be sold using the FIFS model of First come first Serve.
They plan to make Tezos name system to initially support a limited set of characters that will not share lookalike characters with other platforms, this is to help avoid phishing attacks. They plan on launching the service supporting Latin (pure ASCII) names which will be ending with .tez top level domain.
He also stated that they plan on supporting Unicodes later in the future if the risks are reduced.
Other Projects that offer Naming service.
There seem to be a lot of projects with Blockchain Names out there, one notable is the Ethereum Name service which has been integrated with other platforms like Meta-mask.
Other notable projects are NEO, Zilliqa, Name coin etc.