Email which, instead of containing only plain text or rich text, is an HTML document.
A lot of people don't like HTML email as it's usually several times larger in size than a plain text message, sometimes comes with a copy of itself attached, and can occasionally be a security risk.
It's basically an email with an HTML file attached, which contains the message and whatever formatting has been done with that HTML. Services such as AOL are notorious for (among other things) large amounts of HTML email. This can be especially annoying if the whole message is just a sentence or two but comes with a relatively large attachment just so the text can be in purple or some such thing. Some email clients and web-based services have an option for displaying all email in plain text format only. While this avoids the sometimes annoying formatting and possible security risks of the received messages, the HTML version of the email is still present as an attachment so no space is actually saved.
The possible security risk comes from the fact that the HTML email may be referencing a harmful file outside the mail client, which could do some damage to the files on a computer if there's no precaution such as a firewall or high security settings on the mail client in place.