mail password fail (what changed?)

Mail will not receive mail anymore (though it did before, as of yesterday, and I didn't change anything). I can log onto my Gmail account on the server and so I know it's working fine. In Mail, I tried to send a test email to myself. I can send it - I can see it on my Gmail list via the browser, but I cannot receive it. Mail says I need to put in my password. Why? Where did it go? I tried to re-enter the Gmail password (several times) without anything changing; I even tried to put in my Apple password (which I don't think belongs there, but they never specify which password you need - which is irritating - as if there is only one password that you need to be using when you have a web-based email like Gmail on an Apple computer). But that didn't work either.