Page Authority is a calculated metric by Moz’s and declare how good a webpage is in search engines search results.
Page Authority is scored on a logarithmic scale from 0-100 points and function with the relevants links and info within pages of one site to another, Moz always update the algorithm to calculate the PA time to time, so maybe you can see your score fluctuating.
Having high PA on your website gives you the chance to be more visible on search engines and be close to the top position on the first page of search results. To measure your PA there are few online SEO platforms like Open Site Explorer and MozBar.
The search engine algorithms are constantly changing and everybody wants to know how they can rank high, but there’s not much to know really about it because google has released thousands of patterns of the algorithms that tell us how it works.