HTML is a markup language for writing webpages (though it does not neccisarily have to be a web page). This is what you're looking at when you go to internet explorer. All websites use this. As for the web browsing part it sounds like that means simply using a internet browser that uses html.
Mobile web, i think, serves the same purpose as html but is specifically designed to be used on cellphones and other mobile devices. This is much simpler than html.