Nofollow links are ignored by search engines, so that they don't increase the ranking of the target page. It's meant to reduce the impact of, for example, public comments on blogs, which might contain spam links. With nofollow, they don't count for search engine ranking, so that spammers have less incentive to spam.
Nofollow cannot affect the ranking of the site containing the links. If there's a nofollow link within the site, the target page ranking will not increase because of that link, but the 'lost' ranking is applied to other links (without nofollow) instead.
Finally, most SEO practices don't actually affect search engines. Just make sure to create a consistent site for your users, and search engines will do the right thing.