I used to have this with a friend who uses Virgin net, once the new month started he could send and receive again,until he got his settings altered to removed deleted mails off the server.
As Hallmark said earlier, they all count towards the amount of mails in their inbox.
The Inbox is only part of the Mailbox and the Mailbox is only a certain size similar to a Mailbox that mailmen deliver letters to.
IF you just keep leaving mail/spam etc you don't want in it then the box will fill up so mailman can't get any letter in to it!!
The ones you don't want to keep (delete) are still in the mailbox until one deletes them permanently! The reason being, one may "delete" one by accident, it can still be retrieved in the deleted folder.....
Most Programs remove these deleted messages after 28 or 30 days, so makes a bit of space in mailbox until it gets filled again by a few emails UNLESS the messages in the deleted portion of the mailbox are actually removed....
Plus sometimes mail you want gets fitted into Spam folder because that is all the space there is...