Nofollow is a HTML attribute of anchor tag. This attribute do not allow search engine to follow the link only human can follow your link. If any website linking back to you with Nofollow attribute then search engine will not follow your link or in simple words search engine will not consider your link while determining your page rank. Hence that link is useless for you.
Example of Nofollow link-
<a href="http://www.blogger.com" rel="nofollow">Maths</a>
Dofollow is also a HTML attribute tag and it allow search engine to follow the link. Page rank of blog and website is governed by the number of high quality dofollow backlinks created by blog or website on another blog or website, which have good page rank ( page rank 5, page rank 6 page rank 7 ).
Example of Dofollow link
<a href="http://www.blogger.com">Maths</a>
Hope this helps
Shiva.Vnit