Well a key new feature of HTML is the media query. This is something you can add to HTML through the link element, using the media attribute, or to CSS using the @media selector. For instance, you can write:
<link media="only screen and (max-device-width: 480px)" href="mobile.css" rel="stylesheet">
and the file mobile.css will only be loaded if the user is on a device with a maximum screen width of 480px.
It's also a good idea to use the viewport meta tag. For instance, if you do this:
the mobile browser will automatically size the page for the device width.
These aren't really "HTML5" specific things, but new additions to the link and meta tags.