Contextual links are hyperlinks embedded in textual content on a web page. They are also relevant to the subject of the text article/blog. For example, if a web page is talking about home renovation and as part of a sentence contains a link with the anchor text 'renovate my house in Houston', then this link is following the same context as the article text, and is therefore known as a contextual link.
Contextual links make sense to the reader of a page, as they are a highlighted section of the text they are reading which when clicked will take them to another page that provides more details on the subject contained in the anchor text. Not only does it help the user, but it also helps the search engines, by giving an important signal to them that the page being linked to is related to the subject discussed in the surrounding text and anchor text of the link.