Google refers to the technology as a way of evaluating the usefulness, importance, and quality of a website. The PR of a webpage can mean different things for different people.
For a webmaster, a high PR is a sign of accomplishment. It shows that your website is moving in the right direction and has the potential to become successful. PageRank also directly effects your Google search engine listings. Acquiring a higher PR than your competition could mean more traffic for you, and less traffic for your competitors.
Visitors to your website probably won't care about the page's rank. However, visitors who understand PageRank may use your PR as a sign of how credible your content is. Would you rather use the information from a website with 0 PR or a website with 5 PR and hundreds of other websites linking to it?
How is Page Rank determined?
Page Rank is basically determined by backlinks. A back link is when another page links to your page. For every page that links to you, that page is "voting" for you. The more votes you get, the better your Page Rank will be.
However, it gets more complicated than that because some votes weigh more heavily than others. The weight of the vote is determined by the PageRank of the page linking to you. This means that a couple links from pages with high PR could be more beneficial than hundreds of links from pages with low PR. But it gets even more complicated - each page can only transfer so much PageRank. The set amount of PR that the page can transfer must be split up between each "vote" that the page gives out. This means that a PR 7 page could actually give out as much weight per vote as a PR 3 page if it had too many outgoing links.