HTML5, as a standard, is designed to appear the same across browsers and operating systems. Any browser that complies with the standard will render a page in the same way, and will execute any events in the same manner (including new behaviours such as drag and drop). This means that you can be sure when a user clicks on a button, swipes a slider or types in a field, regardless of browser or device, the experience will be consistent.
The information on the page, and the way in which it is displayed (content and style) are distinct and seperate elements. This means that accesibility applications should be able to easily read the content without caring about font size, or colour, or anything that is designed to make it visually appealing. It also means that if you want to adjust the visual aspects of your pages there is a single point of call, the stylesheet, and all pages referencing that stylesheet will be adjusted in the same way.
Multimedia elements, such as audio and video files, can be added to a webpage without any extra coding required, as used to be the case. The HTML5 compliant browser understands what these elements are, and how they are supposed to interact. Also the webpage can now be cached locally by the browser, meaning that additional files and libraries that can be required on a page only download from a website once. This reduces the data transfer and increases the speed in which the webpage loads.