HyperText Markup Language (HTML) is simply a computer 'language' that is used to define the appearance and functions of websites and emails. HTML emails can incorporate different types of fonts, colours, backgrounds, images and hyperlinks.
HTML emails are now supported by the majority of email applications (Hotmail, Gmail, Outlook, Yahoo) and are much more attractive than simple plain text emails. If your email application supports HTML emails then this would be the preferred choice.
'Plain text email' means that only words or rather text characters are transmitted to the email recipient, without any formatting or stylistic information. There are no graphics, colours, different sized letters, or different types of fonts in a plain text email.
Some email programs are not capable of rendering the HTML used for rich formatting in email messages. If you are using a basic email application or have stringent anti-spam security on your network then plain text emails may be a safer option. Plain text emails are also better for mobile devices.