PageRank (PR) is a number calculated by Google which determines the popularity or reputation of particular web page. Its basic algorithm is known, however, it is not possible to precisely calculate this number with some tool because the details are known only to Google. The basic principle is that the number and the quality of backlinks to particular page define its authority. This authority is in measured by this magic number--PageRank. The same applies to the quality of the backlink--the measure for this is again PageRank. The PR for each page is constantly calculated by Google and it is not know to the public. Few times a year Google releases integer value of this number to the public. It can be accessed with Google toolbar, dedicated websites or widgets.
While this number itself does not guarantee high positions in search results it is still a good measure of the quality of the page. The higher the PR the more useful or respected page it is. Therefore it is a good idea to invest some time and effort to raise PR number as high as possible. Another useful property of this number is that it can serve as a tool to quickly evaluate the quality of any website. If you are purchasing a domain or website then the PR number is the first indication of the quality of the site.
The only way to increase PageRank is by getting as many backlinks as possible. In general, every link counts but you should pay attention to at least two things. The first one is the PageRank of pages where you are trying to get backlinks. The higher the PR the more is link worth. In other words, every page passes its reputation (measured by the PR value) to other pages it links to. Therefore, you should look for link opportunities on pages with high PR. The second important fact is the "nofollow" attribute. Links which are marked with this attribute do not contribute to the PageRank calculation and are, from this point of view, worthless. However, link is a link. It points to your page and visitor can follow it. This means that nofollow links still have some value and should not be discarded. On the other hand, the PR value and the nofollow attribute apply only to Google. Other search engines treat links equally.
The easiest way to optimize PageRank value is to get backlinks from blogs, forums, Web 2.0 sites or web directories. There are forums and blogs for every possible niche. All you have to do is to find them. Try to contribute some useful content, posting backlinks to your website should not be the first priority.