Domain mapping replaces your subdomain url with a unique domain name. For example, you could domain map mysite.domain.com to myuniquedomain.com.
You do not need to pay extra in order to accomplish that for your WP MU website hosted at TMDHosting. There is a plugin that you need to have installed on your WPMU website and you also need to park all domains that you wish to use instead of subdomains urls for your subblogs.
In order to have that plugin installed, you just need to contact our tech team by submitting a ticket request.

Please note that you need to own or register all domains that you like to domain map to your subblogs. You can either use your existing domains registered elsewhere or you can register your new domains with us through your client area –> Domain Section.
In order to park your domain names, please refer to the following tutorial:
http://www.tmdhosting.com/tutorials/video/cpanel/cpanel-x3-park.html