What is rel="nofollow"?
rel="nofollow" is simply a cue to the search engine bot that it should not follow this link. Specifically for Google it means that the search engine will not pass on any of the referring page's page rank to the link.
Why Would You Use rel="nofollow"?
There are several instances where you might use this tag. The first is if you are unsure of the reputation of the site you are linking to. This is often done on sites that receive many comments to protect that site's reputation as well as prevent people from commenting with the sole intent of increasing their own site's page rank. Secondly this is done when required by Google's rules. One such rule is that paid content, such as links within sponsored posts, must be tagged with rel="nofollow" to abide by Google's no paid link policy.
How Do You Use rel="nofollow"?
It's easy, though it does require a slight bit of coding knowledge. This is a link in HTML.
<a href="http://thisIsALink.com">This is a link</a>
The same link with rel="nofollow"
<a href="http://thisIsALink.com" rel="nofollow">This is a link</a>
All you need to do is to add rel="nofollow" to the end of your link, that's it! If you are using a CMS like WordPress you will need to switch to the text editor view in order to see your link code (click on the "Text" tab in WordPress).
Where Can I Learn More?
Google, not to mention others, have provided lots of great in-depth information on rel="nofollow". If you'd like to learn more check out these resources: