PageRank is an algorithm used by Google, which assigns numerical value to each webpage. This numerical value shows an importance of a given webpage: higher value, more important page is.
Google uses logarithmic scale from 0 to 10 to assign PageRank values. This means that each level is harder to reach than previous, i.e. going from 3 to 4 is much easier than going from 6 to 7.
So, why check it? Answer is simple. If you own a website, and you want to have high traffic, you need to make sure that search engines consider your website as important one. Here where it becomes important to monitor PageRank and make sure that it does not drop down.