An App password is a 16-digit passcode that gives an app or device permission to access your Google Account, you only have to enter an App password once per app or device, so don’t worry about memorizing it, even when you use 2-Step-Verification.
Note: If you have iOS 8.3 on your iPhone or OSX 10.10.3 on your Mac, you will no longer have to use App passwords to use 2-Step Verification.
When you sign up for 2-Step Verification, we normally send you verification codes. However, these codes do not work with some apps and devices, like Gmail on your iPhone or iPad, Thunderbird, and Outlook. Instead, you'll need to authorize the app or device the first time you use it to sign in to your Google Account by generating and entering an App password. With App password, you only need to enter it once.
Once you are finished, you won’t see that App password code again. However, you will see a list of apps and devices you've created App passwords for.
Note: You may not be able to create an App password for less secure apps.
Every App password is only used once. But don't worry, you can always generate a new App password whenever you need one, even for a device or application you've authorized before. So if you forgot your App password, create a new one.
See full help page there Can’t sign in to my email app