Pagerank is the most famous system for ranking sites. It's used by Google algorithm as an indicator of the importance of a webpage. The exact algorithm is keep secret, but we have an idea of how it works. This post will introduce the basics of Pagerank.

Votes

Here's the official descriptionof pagerank:

Google interprets a link from page A to page B as a vote, by page A, for page B. But, Google looks at more than the sheer volume of votes, or links a page receives; it also analyzes the page that casts the vote. Votes cast by pages that are themselves "important" weigh more heavily and help to make other pages "important."

Basically this means that each time a page links to your homepage, your homepage's pagerank is increased by an amount that depends on the pagerank of the linking page. (that's the reason why webmasters often buy links from pages with high pagerank)

The pagerank increment depends also on the number of outgoing links a page has (a link from a page with thousands of outgoing links is worth less than a link from a page with few links)

Toolbar

Google continuously update the pagerank of each webpage, but values are published every three or four months and can be seen in the google toolbar, with a green bar with integer values between 1 (less linked sites) and 10 (very important sites), with 0 that means "not yet classified"
The pagerank value shown in the toolbar it's not the actual and real value for the page you're visiting, it's just a rough estimation of the pagerank at the moment the values were published (every 3-4 months)

The PageRank value shown in the toolbar is not linear, that is, going from PR3 to PR4 is easier than going from PR4 to PR5 (it should be a log function, with base > 5).

Nofollow

This system of votes increased spams in comments or webpages, as spammers wanted to collect as many links as possible to have better pagerank... so google proposed the nofollow tag to be added to the "untrusted" links (i.e. in comments or places where everybody can add links). There's an ongoing debate on the benefits of the nofollowtag, and the use and abuse of it (wikipedia recently started to use the nofollow tagfor all its outgoing links), but what you have to know is that a link with rel = nofollow will not give pagerank to the linked site.
Here's how a normal and a nofollowed link look like in html:

<a href=www.moneyvsdebt.com> real estate seo </a>
<a href="www.site.com" rel ="nofollow" > nofollowed </a>

Pagerank is overrated

That's true
Pagerank it's good, easy to understand and evaluate, but it's just one of the multiple factor used by google to rank a site: it should not be your first priority, your priority should be the content, then making sure spiders can find it.
If you've good content the backlinks will follow because users will be happy with your content and link back to it... thiswill bring higher position in the SERPs. (Actually, this and avoiding some common mistakes we'll talk about in the future)

Resources

After this brief introduction, you may be intrested in some further and more technical readings about google pagerank and related stuff:

• Google Pagerank on wikipedia
• The Anatomy of a Large-Scale Hypertextual Web Search Engine
  The original paper in which Sergey Brin and Lawrence Page presented the first google implementation
• Information retrieval based on historical data
  U.S. Pantent for Search Engine 125, possibly some hints on google present and future algorithms (This is really a good resource!)
• Pagerank Explained
  Detailed explanation of how pagerank it's supposed to work
• Pagerank Explained #2
  Another similar explanation of pagerank
• Topic sensitive Pagerank
  Proposal for a vectorial Pagerank, with different values for different topics