If you get a message in Apple Mail saying that “the user name or password for ‘imap.gmail.com’ is incorrect” but you know that your email address and Password are the right ones, here are some things to try.

There could be lots of things causing the problem.

I have tried to put the hints that are most likely to work at the top.

• Go to Gmail.com and try to login just to confirm that your username and password are in fact correct!
• On your Macintosh computer go into Mail, Preferences, Accounts  and delete your Gmail account.  Restart your computer.   Add the Gmail account in again.
•  If that didn’t work, do it again but this time  After you click the “+”  button to add a new account, click on “other mail account”  instead of Google and enter the details manually. Here  are the details you need to enter if you are setting up your Gmail account manually: https://support.google.com/mail/answer/7126229?hl=en&rd=1
• Change your Gmail password to one that is more than eight characters long.
• Open Safari on the affected iPhone or Computer and navigate to this page: http://www.google.com/accounts/DisplayUnlockCaptcha
• Login to gmail.com and turn off 2 step verification. https://support.google.com/accounts/answer/1064203?hl=en
• If you want to have 2-step verification turned on for Extra security, you’ll need to make an application specific password for iPhone apps  that don’t support two-step verification.  to do that, log into Google, and under accounts/security/2-step verification go to “Manage your application specific passwords”  This will give you special 16 digit long passwords to use in your iPhone apps that are different from your main Google password
• Change your contacts to “CardDAV”:
  • On your Mac, open the Contacts app.
  • Go to Contacts then Preferences.
  • Open the Accounts tab and click “+”.
  • Fill out the following fields:
    • Account type: CardDAV
    • User name: Your Google email address.
    • Password: Your Google password. (If you’ve enabled 2 Step verification, you’ll need to generate and enter an application specific password –  see above.)
    • Server address: google.com