Some website owners allow emails to accumulate on the server. Once the disk quota of the hosting plan is filled, further emails will be returned to the sender.
Sometimes website owners are unaware that emails are being stored on the server. To correct this, search Google for “leave messages on server” and follow instructions for your email program.
Your disk space can also get filled by uploading large images. This can also cause the “mail box full” bounce message for emails.
Although WordPress optimises images that you upload, it leaves your original image on the server. e.g If you load a 3 Mb image from your camera, WordPress will fit it on your web page at say 100 Kb, but leave the 3 Mb image on the server.
So if you attempt to load 50 images @ 3 Mb each making 150 Mb total, your hosting plan quota will need to be high enough or it will fill up and only some of the images will actually be accepted, or your mail box will be reported as “full”.