1 Pages load extremely fast
Provided that everything was done right amp pages load extremely fast and thus help retain many of the users who would have left because of the slow speed.
2 More search engine clicks (CTR)
Google now ads an 'Amp' label beside sites that are Amp supported. This might encourage users to click on those pages to visit fast sites.
3 More pages views
Given the site loads fast users are more likely to visit more than one page. Amp can thus increase page views in some cases.
4 Search engine ranking boost
There is a wide anticipation that Google will either give a ranking boost to Amp pages or will easier give a ranking boost to fast loading mobile pages. In both cases Amp pages might get a ranking boost.
5 People will get used to fast speeds
In case Amp gains wide adoptions users will adapt to the new fast speeds and those speeds will become the norm. In such a case non-amp sites will appear slower to users. (See Why Google Amp is bad for your site?)
6 It will become the new standard
Amp looks like a successful standard. In case it gains wide adoption then webmasters will be forced to migrate.
7 More purchases
The increased speed might result in more interaction , more clicks and more purchases from the sites that sell products. (See Why do websites have so many ads?)
8 Reaching more people
Amp pages allow webmasters to reach people with slow connections and those who don't have fast browsing speeds.
9 Leads to a cleaner site
Amp forces webmasters to create clean and simplified versions of their sites. This might result in more conversions and better user experience.