Nofollow links attributes do not allow search engine bots to follow link.That means if the website owner is linking back to you with nofollow attributes, it does not pass on link juice.

Do Follow links allow google ( and all other search engines) to follow them and reach out our website. Giving back as backlink or link juice

Do follow links are those links which has the attribute "rel=dofollow" this relation allow the search engines to crawl a URL in a website the link is posted. But the nofollow links dosent allow to search engines to crawl that URL this can be done by the following attribute "rel=nofollow"