(Internet Protocol Address): This number is an exclusive number all information technology devices (printers, routers, modems, et al) use which identifies and allows them the ability to communicate with each other on a computer network. There is a standard of communication which is called an Internet Protocol standard (IP). In laymans terms it is the same as your home address. In order for you to receive snail mail at home the sending party must have your correct mailing address (IP Address) in your town (network) or you do not receive bills, pizza coupons or your tax refund.
There are MANY methods to change your IP address. Some methods will work for you but may not work for someone else and vice versa. If your IP is static, then you CAN’T change your IP address without contacting your ISP.
PageRank is what Google uses to determine the importance of a web page. It's one of many factors used to determine which pages appear in search results.
PageRank measure's a web page's importance.
Page and Brin's theory is that the most important pages on the Internet are the pages with the most links leading to them. PageRank thinks of links as votes, where a page linking to another page is casting a vote.
This makes sense, because people do tend to link to relevant content, and pages with more links to them are usually better resources than pages that nobody links.
PageRank doesn't stop there. It also looks at the importance of the page that contains the link. Pages with higher PageRank have more weight in "voting" with their links than pages with lower PageRank. It also looks at the number of links on the page casting the "vote." Pages with more links have less weight.
This also makes a certain amount of sense. Pages that are important are probably better authorities in leading web surfers to better sources, and pages that have more links are likely to be less discriminating on where they're linking.