First, “nofollow” is a message you can give to search engines through browsers. A browser is a service like Firefox or Chrome or Internet Explorer that takes you around the internet, or goes around and brings things to you (two metaphors, take your pick).
When you make a link at a website, you’re essentially saying, “Hi, there, Chrome, please take people who click this over to another page.” You then give the address of the page.
You can add more information, if you want, with a rel attribute. Rel attributes are ignored by browsers. They are information specifically for search engines. You can use rel=alternate to tell the search engine that you’re just linking to an alternate form of a page (for example, a page that’s designed to be printed out) or you can use rel=next to tell the search engines that you’re linking to the next document in a series.
You can use rel=nofollow to tell search engines that you don’t mean for them to follow that link. Links are considered a vote of confidence by search engines, and normally you would want search engines to follow the link and see who you’re voting for. Sometimes, though, you want to link without making it a vote of confidence.
Webmasters do this for a couple of reasons. First, if someone has paid for a link, nofollow makes it clear that the link shouldn’t be considered a natural link. Paid links, such as ads, don’t count as votes of confidence. Second, you might be linking to a website as a bad example or in order to denounce the owner of the site, in which case your link to that site is certainly not a vote of confidence. You might also have a default policy of nofollow links in all comments at your blog in order to discourage comment spam (fake comments, often generated by robots, left for the sole purpose of getting a link).
“Dofollow” simply means a normal link without a nofollow rel attribute.
Since nofollow links don’t give you that vote of confidence, you’ll often find advice to seek out dofollow forums or blogs and comment at them, while ignoring places with a nofollow policy. There are services like Dofollow Lists which will help you find worthwhile dofollow link sites and you can search for terms like “dofollow real estate blogs” and find lists of blogs that allow dofollow links in comments.
Now that you know what it means, should you care?
The answer is a firm, “It depends.” In general, you shouldn’t care because you’re not going around leaving spam comments whose only purpose is to get a link, right? You’re a good citizen of the online community, you’re networking, you’re saying things interesting enough that people will click through to see who you are or contact you about your services, so nofollow links are just as good for you as dofollow links.
What’s more, your name or company name in a comment might end up on the search engine results page when someone looks for you, whether the link is nofollow or not. This can be a good thing in some cases.
However, sometimes you are actually participating in a community specifically for the sake of linkbuilding. It’s your job, perhaps. As long as you are contributing something worthwhile to the discussion, there’s nothing wrong with that, any more than it is wrong for a restaurant to provide a meal to an organization for the sake of encouraging the members of the organization to use their restaurant.
We’re not shocked that the Powerhouse left their business cards along with the luncheon at the Chamber of Commerce meeting, rather than providing food merely out of the goodness of their hearts. If you answer someone’s question or make a useful suggestion, your company should get credit for it. In those cases, you may still get traffic or other benefits (I once was featured in a Wall Street Journal article after someone saw a comment of mine), but you might as well also seek out dofollow links. There are so many places that you could be useful online that it makes sense, if you’re linkbuilding, to focus on the ones that give you the most benefit.