Page Rank is the system Google's search engine uses to rank search listings and results. When you perform a Google search, you get a list of "search results.Websites or blogs with a higher page rank appear first on this list. Page ranks are given to websites and blogs on a scale of 1-10 (10 being the highest). So a website or blog with a page rank above 6 will more than likely appear on the first couple pages of a Google search. For more information about page rank directly from Google check out this page.
You can attain a very good page rank (above 5) by doing a couple very simple things. However, the direct result of where your listings appear in Google will highly depend on what type of website or blog you are running. If you plan to start a website or blog that is mainly any highly popular topic, it will be more difficult for you to rank higher in search results; because there is already so much competition from more powerful sites. Many of these sites may have been in operation for a significant amount of time, and will have a page rank of up to 9 or 10. It is possible to out-rank these sites, however it will take much more time.