Each account has an associated weak authenticator, much like a weak account key. Someone who has your weak authenticator can attach computers to your account, but can't log in to your account or to change it in any way. This is useful if you need to install BOINC on public computers, or if you want to let someone compute on your behalf without giving them access to your account.
Your weak authenticator is a function of your password. If you change your password, your weak authenticator changes, and the previous weak authenticator becomes invalid.