HTML5 doesn't do anything, per se. It's a spec; one that isn't finished yet. Sure, many of its proposed features will allow developers to produce similar features as Flash, but it's up to the browser developers to implement said specification. Currently, there's a good amount of its proposed spec implemented in different ways by different browser vendors. If your application only uses something that supports some of the HTML5 spec (webkit-based Safari 5/Chrome/Chromium for instance), you can do a lot (ahem, guessing your question stems from Steve Jobs mentioning HTML5 in a Keynote™)...but will struggle with cross-platform support. Many of the major players in the browser market haven't even agreed on a common codec for video yet (H.264 for many, not supported currently by Firefox/Opera/etc. which use ogg/theora) so basically we're going back to pre-flash days of plugin-madness for a bit.
Some of the exciting features proposed in the spec for me are:
canvas for scripting drawings, images, animationsOne of the major things that I personally would find to be a pain to produce using the proposed HTML5 spec: