Private vs. Public Devices
When using this service, the default configuration allows your browser to login to multiple web sites/services without requiring your username and password be entered multiple times. This is referred to as "Single Sign-On". If you're using a machine in a public lab, or a kiosk, or any other shared environment, this can potentially make it difficult for you to prevent another user from accessing web sites on your behalf.
If you select "No" to the private computer / device question, you will be given access to the web site/service you requested, but you will have to re-enter your credentials for any additional service.