The browser and web hosting manager are interacting with the SAFE network (testnet 19 more specifically). The data is stored in vaults running on nodes hosted by MaidSafe in this testnet. In later versions (and in some earlier ones) the vaults will be on user’s computers. The benefits for users are privacy, security, and control of their data. For developers, the advantages are not having to manage the infrastructure for your app, developer rewards, and the ability to make apps that weren’t possible before.