Your quota is the amount of disk space that you as a user get on a server. To see the available amount of disk space, monitoring quota on personal disk space and extra quota, see : How much disk space do I have at my disposal?
When your e-mail quota have been exceeded, receiving and sending e-mail messages is no longer possible until you have deleted enough e-mails. The e-mail quota do not only apply to your inbox but to all mail folders on the server (not local folders). Folders on the e-mail server are e.g. inbox, sent-mail, own folders on the server, trash (depending on the settings) etc.