Backlinks are especially valuable for SEO because they represent a "vote of confidence" from one site to another.
In essence, backlinks to your website are a signal to search engines that others vouch for your content. If many sites link to the same webpage or website, search engines can infer that content is worth linking to, and therefore also worth surfacing on a SERP. So, earning these backlinks can have a positive effect on a site's ranking position or search visibility.
Earning and giving backlinks
Earning backlinks is an essential component of off-site SEO. The process of obtaining these links is known as link earning or link building.
Some backlinks are inherently more valuable than others. Followed backlinks from trustworthy, popular, high-authority sites are considered the most desirable backlinks to earn, while backlinks from low-authority, potentially spammy sites are typically at the other end of the spectrum. Whether or not a link is followed (i.e. whether a site owner specifically instructs search engines to pass, or not pass, link equity) is certainly relevant, but don't entirely discount the value of nofollow links. Even just being mentioned on high-quality websites can give your brand a boost.
Just as some backlinks you earn are more valuable than others, links you create to other sites also differ in value. When linking out to an external site, the choices you make regarding the page from which you link (its page authority, content, search engine accessibility, and so on) the anchor text you use, whether you choose to follow or nofollow the link, and any other meta tags associated with the linking page can have a heavy impact on the value you confer.