"mail" usage

I used to access my gmail account through mail application on dock of my desk-top Mac.

Since the end of May, I can only access to my gmail account through my google account on Firefox and it works well. If I try to use “mail” on the desktop, it no longer works as before. The emails in the mailbox would not updated and I can’t send out email as before. When I tried to send a message out, a pop-up box shows: “Cannot send message using the server Gmail, application-specific password required. Also It shows ‘Gmail(Offline)’.

I had the 2 step verification turned on.

I have a Mac OS X version10.9.5

[Email Edited by Moderator]