Short Answer: Link Building is the art of getting other websites to link to your website, webpages, or documents in a way that increases the value of your website, webpages, or documents in a search engine’s algorithm.

Full Answer:
Link Building is an essential component of SEO work which seeks to impact one of the main underlying factors of Google’s search engine ranking algorithms and of algorithms used by other search engines that utilize the links between web documents (i.e. Bing and DuckDuckGo) as a way to help rank documents. Link Building was not an essential SEO component until Google’s search engine debuted in 1998.

Essentially, Link Building is a rather simple concept. Your goal is to gain a hypertext link (in HTML code) from another website or document to your website’s homepage or a desired document on your website. This helps search engines understand a variety of things about your website and the documents on your website including how popular your brand/domain is, what keyword(s) the document on your site is relevant for, and how much an algorithm should trust your website.

While Link Building sounds simple, it has become increasingly complex and difficult to gain new links that will help a website, webpage, or document increase in rankings within a search engine (especially Google). In the late 1990’s and early 2000’s gaining new, valuable links, was often as simple as sending an email to the webmaster that owned or maintained a site/webpage and requesting the link addition. In some cases this was actually an automated process through link directories, reciprocal link programs, website directory listings, and article link building. All of these types of link building have largely been devalued or outright penalized by Google’s team of search engineers in an attempt to ensure only links of a high caliber that are granted via editorial discretion are counted by their system.

The PageRank Algorithm
Link Building was made essential for SEO by Google’s most novel and first innovation in search results rankings: the PageRank algorithm. This is the algorithm that was written by Google’s founders Larry Page and Sergey Brin while attending Stanford. The algorithm essentially provided an ever-changing score to each document on the web which is calculated by examining all of the scores coming from all of the links pointing to the document. Google used to provide a version of this score publicly, known was Toolbar PageRank (TBPR), however they stopped updating this public metric in the early 2010’s and eventually fully deprecated it in 2016. While the public version of the metric is no longer available, Google employees have made it clear that some version of the PageRank score is still widely used in Google’s calculations of the value of documents on the web and most SEOs consider it to still be one of the top ranking factors if not the most important one.

PageRank made Link Building a necessary component of Search Engine Optimization and the tactics SEOs use to gain new links makes it necessary for Google to constantly find ways websites are gaining links that Google believes are dishonest or manipulative and to either devalue or penalize those. This escalation has forced SEO professionals to constantly seek out new ways to convince other websites to link to theirs either in unnatural ways search engines like Google may not yet know how to discover and devalue or in natural ways that may present more challenges, take more time, and provide less immediate value.