I want to publish my website and I don't know which host to choose. A free host which has "Mailbox quota: maximum-500", and a paid host which has "Mailbox quota: unlimited". What does mailbox quota mean and how much represents 500? Mb of emails or I can send maximum 500 emails?
Most of the mail servers have a storage limit that you cannot exceed.
If your mailbox has a quota set to 500MB, once the limit in size is reached, you will not be able to receive emails since the mailbox would be deemed full.
However, if you get unlimited, you will never actually fill up your mailbox.
Keep in mind, as long as you are regularly cleaning out your email account, having a quota would not be an issue, since you're deleting the emails.
Attachments do count towards the quota as well, so if you receive a lot of large files such as images, it may be wise to have unlimited.
Just using ballpark figures from my current email server, without attachments you should be able to store over 10k emails on 500MB of space.