A popular security measure is "two-step" or "two-factor" verification. This is a method of signing in by entering your password then you receive a text message with a second verification code. The expectation is that only you will have access to your phone and the code proves it is you.
It works pretty good and is not overly annoying when you use web mail, provided you don't clean out the cookies when you close the browser. If you do, you need to enter the code every time you check email.
When you are using 2-step verification with Gmail, Outlook.com, or other email provider, Outlook (and most other mail clients) do not support using a verification PIN. You need to use an application specific password instead of your real password and the verification PIN.
In Gmail, the link to application specific passwords is at Gear icon > Settings > Accounts > Other Google Account Settings > Security.
In Outlook.com, look for the link to two-step verification at Outlook.com's Gear icon > More Mail Settings > Account Details > Security Info.