Nofollow links are those where you are linking to a website you don't trust 100% and want to tell search engines that "Geez... you know, I might have linked to that website but I don't exactly trust it.". However, being a software developer myself, I am willing to take a bet that Google engineers will consider a website to be good when it has a balanced number of nofollow and dofollow links and not only a certain type of links which might actually go against Google Webmaster guideliens.
Google has also said that they will still count the nofollow link as an outgoing link in terms of the distribution of page rank from your page.
When another website links to yours with a standard link, it can directly affect search engine rankings.
However, nofollow links include a small piece of code, called an attribute, that lets search engine bots know not to follow the link and not to pass any link equity. It looks like this: rel="nofollow".