Your Ripple wallet contains your secret key and your contacts in an encrypted form. Your balances and configured credit lines are stored in the ledger in the distributed ripple network. Currently there are only a dozen or so ripple servers all under the control of OpenCoin (in order to make it easy for them to make changes during the beta to the server code that would otherwise disrupt the network). As long as there are a sufficient majority of ripple servers intercommunicating you only need to be able to communicate with one of them (bitcoin is vaguely similar in that there is an intercommunicating network or bitcoind processes). Currently the webclient connects to
s1.ripple.com by default (look under
Advanced->Options) presumably this could point to any ripple server, and perhaps once out of beta the clients will have a list of servers to try.
When you created your wallet and when you login with the webclient there is a "Fetch Wallet" option (see What do the "Fetch Wallet" options when opening a Ripple wallet mean?) that controls where the wallet is stored. By default an encrypted version is stored "in the cloud" and locally by your browser. With the default options, if you run the webclient from the same machine+browser it can use just the local copy if the cloud storage is unavailable. If you move to a new machine or a different browser, the copy in the cloud needs to be accessible. You can also make a local backup of your wallet to a file, see How do I backup my Ripple wallet?
If for any reason there is no copy of your wallet available, all is not lost. Ripple lets you create a new wallet using your existing secret key (which is why they strongly recommend making a copy of the secret key). Since the wallet only holds your secret key and your contacts, all you will have lost is your contact names. The client would show your trust/credit lines and transaction history using just the ripple addresses of others. You'd just need to re-enter the contact names (perhaps recognizing your contacts by your current trust/credit limits and balances or perhaps needing to ask your contacts again for their addresses).