DA and PA are Moz metrics not google ones. That's the first thing to note. Moz recently made some changes to their way of calculating the metrics that made them a more accurate predictor of the ranking capability of a page.
So basically they are an integer that's arrived at by a calculation involving the number of links pointing to a page and the power and authority of those links. DA is global, so one domain in the pond of the whole internet and PA is a local to your individual site. So each page you own in the pond of your whole site.
So how do you use these metrics?
- find out whether google is ranking links and a pages 'power' or the content therein. Sometimes the first three results all have very high DA of 60-70 and 80+. This means that to compete you'll probably need to get a ton of links to your page to be in that top three.
Other times the top three can have little or no domain power and just be great articles. This is more common now.
- You can look at the PA or your individual pages and rank them according to PA. Then see where each ranks and whether there are any statistical outliers. Sometimes a page with low PA will be doing well. That's great. Other times a page will bomb and if you find that it has a low PA then you might want to insert some internal links to it to bump it up a bit.
By way of additional research look here:
https://moz.com/blog/the-new-link-explorer-is-here - rand on DA updates
https://www.mattcutts.com/blog/pagerank-sculpting/ - matt cutts on pagerank
https://www.searchenginejournal.com/pagerank-patent/250603/ - roget montti on pagerank patent and lots of _science, yo. _
Go get em!