It's not possible to password protect the ONE, Groups, or Enterprise application when it is open and running, but you have the option to for the application to ask for your account password before it will launch. This is done through enabling the option "Ask for password at startup", which is found at Preferences - General.
Do keep in mind that being a backup tool, SpiderOak copies files on your local computer; it does not remove them. Asking for your password at startup will keep nosy people out of your account, but keeping the files on your computer safe from snoopers is your responsibility.