“Add a device” enables you to sign in with an existing email address on a different device than the one where you had initially set up your wallet. Whenever you need to access your wallet that is created by your email id on a new device, you will need to add that device using this option. This needs to be done only for the first time. Please note that even a different browser on the same desktop is considered as a “new device”.
For example, you created your account using leapiscool@gmail.com on your desktop and want to log in with the same email on your mobile. You need to add your mobile to log in and access the same account.
Check out this FAQ to learn to Steps to Add a device