What people loosely refer to HTML5 in the context of this discussion is the combination of HTML as a markup language, CSS which specifies how it is rendered, and the javascript code which manipulates the HTML and CSS dynamically.
Furthermore, HTML5 not only has the standard text elements, but also on which 2d graphics can be drawn, and elements which embeds the video (as the name suggests).
So, in a full-fledged implementation of HTML5, you can implement dynamic web sites without using Flash. An example is the HTML5 version of Youtube, recently introduced as beta for Safari/Chrome users, see here. Another is an NES emulator in javascript + HTML. (Well the latter does not really concern HTML5... it uses .)