Yes, a website need to have combination of both Dofollow as well as Nofollow links. Having only Dofollow or only Nofollow links can negatively impact your website. As far as ranking as concerned, Dofollow links help to increase the website ranking and traffic but Nofollow links are more helpful to increase the brand awareness and to generate traffic.
Do-follow links are the links which are indexed by web crawlers so they are good and effective for SEO while No-follow links are the links which are not indexed by web crawlers so they are not much effective for SEO.
Do follow links used to increase the website traffic on search engine. Search engines crawl only do follow links of a website. so SEO professionals focus more on do follow links to build quality backlinks.