Google's definition can be summarized as:
PageRank is based on the Internet's democratic nature and utilizes web link structure as an indicator of an individual page's value network. The main element of the algorithm sees a link from page A to a page B as a "vote" on the website of A to B. The number of "votes" are crucial to the PageRank value Google gives to website B. Google also analyzes website A, and if this website is considered to be "significant" then website B is given an even higher value. Many inbound links from other highly ranked and significant pages can provide website B with a higher PageRank.
An attempt to explain this in a simple way would be to say that Google ranks the importance of your webpage compared to others. This is done on a scale from 1 - 10 The reason that Google ranks your page is to provide people who search on Google with the most relevant content according to their search. Sites that have a lot of traffic and many links to them will often have more relevant information than small sites with low traffic.
What gives my website higher page rank?
- Inbound links from other websites. An inbound link from a site with high pagerank matters more from a site with a low rank.
- Many visitors to your website.
- Age. A new website is not as highly ranked than one that has been online for a while.
- Good technical quality of the page.
- Frequently refreshed pages, or pages that frequently have new content.