The PageRank value for any URL can be understood pretty well by thinking about a "random walk" around the web:
Begin on any old web page -- anywhere at all.
Click on a random link somewhere on that page.
Continue doing this indefinitely.
PageRank is the probability that you will eventually end up on that URL.
So, if a URL has a PageRank of 5, then there is a 50% chance that your random walk will eventually take you there. And moving up from a 50% chance to a 60% chance takes a lot more links than moving from a 10% chance to a 20% chance would require.
The mathematics that Google uses to create their model for this "random walk" has changed several times since the original formula was published, and the details of those changes have not been made public. For instance, my guess for one change is that a "random link" in step 2 is no longer strictly random. Instead, it is weighted according to what area of the page actually holds the link. The original formula did no such weighting.