MozRank represents the popularity based on links to the url. It is similar in concept to how the Google Page Rank is calculated. Pages earn MozRank by the number and quality of other pages that link to them. The higher the quality of the incoming links, the higher the MozRank.
MozRank is continually updated, the Moz page rank results shown are updated frequently. Google updates their page rank frequently also but has stopped updating the page rank shared with the public.
MozRank is based on a logarithmic scale (as are Moz page authority and Google PageRank). This means a value of 4 is 100 times a value of 2 and a value of 7 is 1000 times a value of 4.
Moz also provides a Page Authority value which is meant to enhance the straight Moz page rank based on a number of additional factors.