Twitter like many other services now has a two-step verification or two-step authentication that you can use. Once you set this up, the next time you want to login to Twitter. In addition to providing your password - a security code will also be sent to your phone. This code will need to be entered before you're granted full access to your account. This is good news because of the numerous accounts on Twitter that have been hacked. Out own Twitter has also been broken into during the last phishing attack on Twitter. With 2-step verification; Twitter seeks to add more security.

How to turn on, enable, or setup Twitter 2-Step Verification
1. Login to Twitter
2. Click on the Gear icon and choose settings
3. Scroll all the way down and tick the box before 'Require a verification code before I sign-in
4. You will be sent a message on your phone.
5. If received click 'Yes'
6. Save Changes.

Your login verification on Twitter is setup. Next time you want to login a verification code will be sent to your phone. Only after entering this code will you be granted access to Twitter.

To disable login verification on Twitter follow the above steps and simply uncheck the verification box.

You might also like - How to setup Gmail 2-Step verification

Please check video below for visuals.
http://www.youtube.com/watch?v=5cXoUQ1wG7g