PageRank is an algorithm used by Google for link analysis. It was invented by Larry Page and Sergey Brin; the owners of Google. It was developed by Google to rank pages on their merit and not on meta tags as people had started misusing meta tags to improve their rankings. It evaluates the quality and quantity of links to a webpage and accordingly assigns a score on a 0 to 10 scale based on the page's importance and authority.
It is an important off-page optimization factor. It decides how easily and quickly your users can find your webpages on the world wide web. If your PageRank is good the user will find you easily as the search engine will keep your site higher on the search engine listings.
It is calculated by a proprietary mathematical formula that considers each link to a website as a vote. A website is compared with every other website with similar content and keywords in a popularity contest. The website with most links including the most valuable links gets a higher rank in popularity.
So, to improve the pagerank of your site, your website is required to have backlinks from other websites. Each link or vote to your site adds value to your site. Google also evaluates the websites who offer the link to your site.