You may be asking, "Why can't I access my data right through the website?". The answer is simple: Your privacy is important to us. To access data through a website requires that a web server sends data to a browser. In other words, Wuala's web server would have to decrypt your files so that they can appear in your browser. However, all your data on Wuala is encrypted directly on your computer. Further, your password never gets transmitted, so that no one - not even Wuala as the provider - can open or read your files. Thus, you can only access your private data with a local desktop application that can read the file(s). For your convenience, this desktop application can be started directly from the web by clicking on the button above - no download or installation required.
In short: All browser based services have access to your data. Since Wuala's security mechanism doesn't allow access to your data, your data cannot be accessed through the website.