On-page mobile SEO is all about higher mobile SEO rankings on Google by optimizing individual web pages. First and foremost, keyword research and then looking at on-page mobile SEO elements: Title tags; Meta description; Image alt tags; URL; H2, H3 subheading tags, etc.
Off-page mobile SEO is all about improving your site’s Search Engine Results Page (SERP) by using the following techniques: Building links; Social media shares; Brand mentions; Email outreach, etc.
To simplify it, what happens inside your website is on-page mobile SEO, and what happens outside of your website is off-page mobile SEO.