They pertain to backlinks.
A "do-follow" link, which is just a regular link without an attribute, tells search engines to follow the link and pass on link equity.
On the other hand, a no-follow link, which is a link with a no-follow attribute such as the one below, tells search engine not to follow the link.
Code:
<a href="URL.TLD" rel="nofollow">Anchor Text</a>
In case you're wondering why someone would no-follow a link, you can read about it below.
https://support.google.com/webmasters/answer/96569?hl=en
Here are a few additional resources you can use to learn more about do-follow and no-follow links.
https://www.woorank.com/en/p/link-juice
http://www.shoutmeloud.com/understand-********-nofollow-link-seo-basics.html
https://moz.com/blog/the-hidden-power-of-nofollow-links
https://en.wikipedia.org/wiki/Nofollow