HTML 5 is the latest revision of HTML and like HTML it is a standard used to create web pages with code.
Flash, an Adobe product, is a platform that adds animation, interaction, and video to the web but it's not a standard and requires a plug-in to run.
There is a heated debate going on about which direction to go in...basically Apple vs. Adobe. Apple first refused to use Flash on ipads, ipods, and iphones creating an out roar from Adobe and also the Flash developers as they worried about their livelihoods. HTML 5 eventually would be able to do all that Flash does now for websites but without a plug-in making it a cleaner way to build a multimedia website and improve security.
Apple's initial decision to ban Flash from their devices seemed to be a selfish strategy to dominate the App sales. This isn't to say that we shouldn't progress and move towards HTML 5 but that it is monopolistic to ban Flash from certain devices and discourage it's use when you have as much commercial dominance as Apple.
All applications should be open to designers so they can pick and chose what they want to use. HTML 5 is brand new and isn't fully developed yet, designers need a chance to use it and find the advantages and disadvantages. Often designers need to use multiple applications to achieve what they are going for in terms of specific audiences and their creativity shouldn't be stifled by giant corporations like Apple. For a company that prides itself on innovation and creativity, it is good that they are looking towards the future but they should allow adaptions for Flash, to serve their customers best. After all isn't that what it really should be about?
Check out the debate: