rel="nofollow" and rel="dofollow" are link attributes. They will tell the search engines whether you allow them to index or crawl the links you have included in your posts, sidebar, or footer (whether it links to your pages, or outbound links, or social media links such as twitter and facebook)...
Commonly, the nofollow or dofollow issue happens a lot in your outbound links a.k.a your sources. Most of the times, when you publish contents, you include links from external sources. The question is, would it help you or not?
Hence the nofollow and dofollow are created to somehow safeguard publishers. If you are not sure that what you are linking is safe enough for your reputation, then try putting nofollow to the link that looks like this in your HTML post editor: <a href="the url of the site your are linking" rel="nofollow">anchor texts</a>, the nofollow attribute there tells the search engine to disregard that particular link when it is indexing your site... oh I, I am referring a lot the way Google indexes your pages.
But if you opt to pass your PR juice to the site you are linking, then feel free to use nothing, I mean if it's dofollow, leave the link as is without putting dofollow.
The real question is, when to put nofollow?
Somehow people are afraid about placing links to their pages, but the real deal is - if you are linking to trusted sources, and if you are linking to links that has contents that is important to expound or elaborate or support your topic - then do not be afraid to pass your link juice by not placing nofollow attributes.
Yeah, Google loves justice. If they know you are linking to relevant contents outside your webpage, nothing to worry about....