When you link your site to a do-follow site the html link code will be a regular anchor text html link.
In the case of a no-follow the no follow html tag will be added within the link and you would not get a link back to your site from this site.
If you link your site to a do-follow site the search engines will acknowledge your link and you will get what is called a backlink to your site.
If you link your site to a no-follow site the search engines will not acknowledge the link as a backlink to your site.
What does this mean for you? If you want to build backlinks to your site and get a higher PageRank you need to make sure that you are linking to do-follow sites, which includes most high ranking sites with a high PageRank and high authority.
If a "do follow" designation is made, Google will look at the link as a backlink to your targeted page.
If a "no follow" designation is made, Google will not use it as a backlink to your target.
There are Do-follow and No-follow article directories, blogs, and social networking sites.
Just by doing a simple Google search you can find out what there are.
Sometimes, No-follow sites are still valuable for traffic to your target, despite the fact that Google may not count it as a backlink, and there are some that argue that a no follow will still give you a little backlink juice.
However, it is always better to make sure to what kind of site you are linking your site too, especially if it's a site that you link to on a regular basis.