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PageRank (PR for short) is the method by which Google evaluates the importance of any given site. Pagerank is Google’s way of deciding a page’s importance.

Google assigns a numeric weighting from 0-10 for each webpage on a logarithmic scale (like Richter scale), meaning that the gaps between the integers increase logarithmically the closer you get to 10. So, for example, the gap between the 2 and 3 is quite small, whereas the gap between 7 and 8 is huge in comparison. As such, boosting your PageRank from a 2 to 3 would be quite easy, and going from a 7 to 8 would be quite hard.

Does pagerank only matters for getting a high ranking?
No. pagerank is not the only thing that matters, things like keyword density, and the anchor text used to link to the site will also have varying degrees of effect on Google.

But somehow pagerank matters because it is one of the factors that determine a page’s ranking in the search results. It isn’t the only factor that Google uses to rank pages, but it is an important one.

At one point, PageRank (PR) was a major factor in rankings. Today it is one of hundreds of factors in the algorithm that determines a page’s rankings.
Google updates its algorithm regularly to keep its results relevant. So, the formula used to determine pagerank and Google rankings is not constant.

Alexa Traffic Rank:
This is a ranking system set by alexa.com (a subsidiary of amazon.com). Alexa traffic rank gives rough indication of the traffic your website is getting. The traffic rank provides historical traffic data. The traffic rank number gives the three months aggregated data from millions of Alexa Toolbar users. And it is a combined measure of page views and users.

The lower your rating on Alexa the better. If you have a ranking under 100,000 then your website should be getting good traffic. 3,000,000 to 4,000,000 ratings are for new sites mostly, or sites with no traffic basically. While a rating of 1 will be for the website with the most traffic.

Alexa’s objective is to show the actual traffic of a particular website, the number that it shows serves as only a random sample of the actual traffic of that website. This is because only a small percentage of internet users are using Alexa toolbar, where Alexa Traffic Ranking algorithm solely base its computation and ranking. In addition to this, Alexa Toolbar works only with the Internet Explorer browser and on Windows operating systems.

Thus, Alexa Traffic Rank has a considerable percentage of error and doesn’t really reflect the exact and actual traffic of a website. But since the traffic was base on a random sample and assuming that the sampling is close to uniform, it could still be a good bases for giving idea of the amount of traffic and traffic ranking, just always remember that it has some percentage of error.

Google Pagerank and Alexa Traffic Rank though both attempted to rank the websites. On the other hand, they are entirely different in their objective, (Google rank web pages according to its popularity and importance based on inbound links while Alexa rank the websites according to its traffic, which is randomly sampled). That is why it is more often that they show a different and contradicting statistics, specially, for a relatively small and new websites.

Source: Marvist.com