Contextual links are links which connect you to a relevant site within the body of the text.
There are primarily three kinds of contextual links, namely: external links, internal links and reciprocal links. While external links (also called outgoing links) carry you to another website, internal links move you to a piece of content within the website.
Reciprocal links are cases where two websites come to an agreement to link to each other. Backlinks refer to those links which refer to your website (these are also called inbound links). The popularity of your website will be determined by how many backlinks refer to your website. Backlinks form a core brick in SEO as many search engines (particularly, Google) will give more merit to those websites, which are backed by many quality backlinks and rank them more relevant than others during a search query.
When a website refers and sends the audience to your website, then it passes the link juice, which decides the rank of the article and also enhances authority of your domain.