Ripple makes a clean separation between the core functionality and the UI. The core functions are carried out by the Ripple server, rippled. The Ripple servers are all interconnected and form the peer-to-peer network.
A client can connect to rippled either running locally or across the internet. One Ripple server can serve many clients. Neither the Ripple clients or the Ripple servers need to trust each other. The Ripple API describes what commands and requests the client can issue to the server.
Clients can store their account info and other data or if they want to access this data from multiple computers and devices they can store this info in a Blob Vault. See Credentials.