Nofollow is an HTML attribute value used to instruct search engines bots that a hyperlink should not influence the link target's ranking in the search engine's index.
Whereas
Do-follow links are highly recommended for SEO purpose. It is utilized to improve the website PR on the search engine bEcause the link which is index by crawler are called do follow link

No Follow links are does not follow the link juice but its used to increase website traffic.And Do follow links are given backlinks.

Nofollow Links are the links which are non crawlable and tells crawlers not to follow. Dofollow links are crawlable links and tells search engine bots to crawl and follow the links.

Dofollow links are more important. They will crawl all your link.
Nofollow links wont crawl

Both ate useful but search engine always gives first priority to the do follow links.

Links that point to another website are called do follow links and pass link juice to a page that help to increase itsranking in search engines.

A no follow link is a link that doesn’t point to another site. I think this is where people get confused, as people can still click onto a no follow link and get sent to another site, but in the eyes of the crowler they don’t point to othe sites.

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

Google

Dofollow links - Dofollow links allow google (all search engines) to follow them and reach our website. Giving us link juice and a backlink.

Example of Dofollow Link:
Google

NoFollow links do not let link juice pass from the site giving the backlink to the original website. DoFollow links pass on link juice from one website to another.

Links that “point” to another site are called do follow links. These pass link juice to a page, help to increase its PageRank and raise its profile to the search engines. The more natural do follow links a website has, the higher it is likely to rank online.

A no follow link is a link that doesn’t “point” to another site.I think this is where people get confused, as people can still click onto a no follow link and get sent to another site, but in the eyes of the search engines they don’t “point” to anything.

A Do follow link that count as points, pushing SEO link juice and boosting the page rank of the linked-to sites, helping them go higher in the SERPs as a result.
A No follow link that does not count as a point in the page’s favor, does not boost PageRank, and doesn’t help a page’s placement in the SERPs.