Managing personal Outlook.com account settings, security, and privacy
Like many here, I was also confused about this new storage limit scheme by Microsoft. I have a few email accounts for various uses and 3 of them have the over storage limit message. I just ignored them and emails were working as usual, until today when people who tried to email me got their emails bounced back with "mailbox full" errors. I had no choice but to start archiving older emails.
The sheer stupidity of all this is that I am under my 15 GB limit, but attachments apparently are being counted towards your 5 GB OneDrive limit. I don't even use OneDrive!