MozRank quantifies link popularity, based on a 0 to 10 scale. MozRank shows the importance of backlinks (i.e. inbound links). This is calculated by the number and quality of the web pages that link to your site.
The Moz algorithm measures both the quality and quantity of links. Each page has its own MozRank.
In general terms, the greater the number of in-bound links, the higher your MozRank will be.
In addition to MozRank, Moz provides a Domain Authority score.
If you subscribe to their service, they provide Keyword ideas, Competitor analysis, Website crawl and audit, as well as other services.
Moz was founded in 2004 which means that it is one of the older SEO services – however it is a well respected name in the world of Search Engine Optimisation.