(see also NoFollow)
TL;DR
A “follow” link is a type of backlink that sends authority to the quoted source without using a blocking tag such as rel=”nofollow”. A “follow” link is not highlighted in any way and is defined by the absence of “nofollow”.
What is a Follow Link?
A follow link is a backlink created by websites without using a rel="nofollow" HTML tag that would otherwise instruct search engines to ignore that link when crawling is done. Contrary to what some may believe, there is no rel=”follow” tag to act as the opposite of the rel=”nofollow” tag. A follow link is simply a hyperlink that is not using rel=”nofollow”. This type of link will pass on authority to the web page it is backlinking to, making it more useful for that pages’ link building strategy for SEO. While the rel=”follow” tag can be added to the hyperlink, it will not have any effect whatsoever.
Update: as of September 2019, Google seems to have changed the way it interprets “follow” and “nofollow” links. It has been suggested that Google may start taking into account “nofollow” links in some cases, regardless of the instructions coming from the website where the hyperlink is.