HTML5 is the latest version of coding technologies used within website building. It allows rich features such as video and animation to be supported without the need for plugins such as Adobe Flash. It also enables more advanced browser functionality, such as drag-and-drop of files from your desktop directly to the browser (you may have seen this used by Google, WordPress and Dropbox).
As plugins such as Flash are no longer supported by all platforms, HTML5 increases the chances of all web users being able to view the content on your website. After all, the last thing you want is for someone to browse to your site and be presented by a blank box rather than your site content!
Read more about HTML5 and see some examples here: https://www.unleashed-technologies.com/blog/2011/12/19/html5-review-will-html5-replace-flash