Hi, Do-follow is the just opposite to No-follow. When it is given as rel="nofollow" in the HTML tag then it is called No-follow, that means you get a backlink from that site but that sites page rank is not traversed to your site. So, it is preferable to get back link from Do-Follow site than No-Follow site.
Do-Follow is nothing in HTML code.you may search in w3schools web site too. No follow attribute is introduced by Google only that means Google Bot will not crawl over the link which has rel="no-follow" attribute,remain search engines like Yahoo! and Bing do not support this link attribute.