Managing personal Outlook.com account settings, security, and privacy
Is your "Outlook icon" a shortcut to the Outlook.com web site that opens your web browser, or is the icon for Microsoft Office Outlook, a personal information manager installed on your PC?
If the former, then the next time you're finished using the web site, click your account name and choose "Sign out" from the drop-down menu that should appear. This will erase the cookie on your PC that is holding your session status, causing the web site to ask for your credentials the next time you connect. When you do, do not check the box that says "Keep me signed in" and the issue should not recur.
If, however, you are using Office Outlook, then tell us what version. Your account settings should contain a checkbox that tells Outlook to remember your password. Uncheck that box and you'll be prompted for it each time.