On-page SEO is something that optimising on your website visuals, content, texts, images, css and html codes etc. to assure better browsing experience for the users. Yes, now better user experience means good ranking in search engines. New search spiders are good in identifying your website's ease of use. Mobile user experience also includes in onpage SEO.
Off-page SEO is all other activities outside of your webpage to encourage better traffic to your website. Examples of off page SEO are social sharing, link building and other offline activities to promote traffic to your website.
In order to get better search rankings one must concentrate on both on-page and off-page SEO. It's because no one is there to interact with a crappy website or poorly designed webpage even if how good SEO is done for it. So as search engines too.
So on-page optimisation is very important together with off-page optimisation.
Newer search engine bots are much like human and has the ability to analyse the content and intend of your website. So whenever you make a webpage make it for your users. Unique and usable content will surely make good results in search rankings.