Hi TPLP4403,
Welcome to the Apple (user-to-user) Community!
Wondering if the message comes from Apple ... or from your eMail provider.
You may want to sign in to your account on your email provider's website (eg Yahoo / GMail etc.) and see if you are exceeding their storage limit with undeleted emails.
(You may be able to use settings to delete email there as you delete email on Mac)
Else perhaps the memory / storage on your Mac is so full your Mac is not operating smoothly. (Eg: a Mac generally needs around 50Gb free in which to do everything you ask it to.) See used and available storage space on your Mac - Apple Support
If you find your Mac is short on space, it is wize to back up all your data eg: to an external hard drive, before deleting anything. That way you can retrieve anything if you find you need it. Eg: Back up your Mac with Time Machine - Apple Support
How to: Free up storage space - Apple Support
NB: Remember to empty the bin on Mac, in order to see the reclaimed storage space.
All the best :-)