DoFollow Versus NoFollow
When it comes to passing link juice, there are two different types of links: DoFollow and NoFollow. DoFollow links are links which pass link juice, or in other words influence in regards to search engines from one page to another. Conversely, NoFollow links are those which don't pass on any influence so they won't effect your rankings.
Back in the earlier days of the internet, most links were DoFollow. It was only when search engines began using links as a major ranking factor and link building was subsequently exploited they came up with the DoFollow versus NoFollow system. Nowadays, most links are NoFollow by default and it's getting more difficult to find DoFollow links.
Now you may be thinking that you shouldn't waste your time pursuing NoFollow links if they don't pass any search engine influence, but NoFollow links still have their purposes.
Most importantly, NoFollow links are still functioning links, meaning you can still get a good bit of traffic from a NoFollow link. Furthermore, any traffic you do get from a NoFollow link could always end up garnering you more links/traffic from webmasters in that initial traffic you get, and some of those could potentially be DoFollow links. Basically you would or should never turn down a link just because it's NoFollow.
NoFollow links are also important for SEO because, while they don't pass on any influence, Google likes your link profile to have a nice mix of both Do and Nofollow. If you're only getting DoFollow links, that says to Google that you're only looking for the search engine benefits they offer, in other words it looks unnatural and can actually keep you from growing in the SERPs.