SEO and PageRank are intertwined. You can even argue that PageRank laid the foundation for the SEO industry; and for Google.
PageRank is the main reason why Google succeeded in overtaking the conventional search engines at the turn of the century. It was created way back in 1996 by Sergey Brin and Larry Page, the two founders of Google. Page had a theory. Counting the number of links pointing to a website was a way of ranking that site's popularity. While popularity does not necessarily equal quality, Page and Brin believed it would be a valid indicator, like the number of citations in academic work. So, PageRank - named after Larry Page - is an analysis algorithm that assigns a numerical weighting to each webpage based on the value of the webpages that refer to it. Pages with a high PageRank through a high number of quality backlinks are perceived as more trustworthy by Google and thus rank better than those with a low PageRank. This is how Google explains PageRank:
"PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. The underlying assumption is that more important websites are likely to receive more links from other websites."
This approach revolutionised the search industry and sent Google way ahead of search engines at the time, such as HotBot, AltaVista, and Excite. However, smart web admins and other clever folks recognised that they could affect the search results by getting many websites to link back to their sites. Thus, the SEO industry began. Google started gradually removing information about PageRank because it had created a whole market for valuable links that were traded among websites to get a higher ranking. Over time, Google's algorithms became more sophisticated and contain various parameters today But PageRank remains an important part of Google's way of ranking web pages.