Connecting your mobile number to your Twitter account will allow you to:
Congratulations! You can now send and receive text messages (SMS) updates via Twitter for SMS!
Once you've added your mobile device to your account, check the box at the bottom of the mobile settings page for added account security. If you ever forget your password or lose access to your account, you will be able to send yourself a password reset via SMS.
Our troubleshooting article has answers to common problems with with using Twitter for SMS.