The primary one is consistent, defined error handling. As you know, HTML purposely supports 'tag soup', or the ability to write malformed code and have it corrected into a valid document. The problem is that the rules for doing this aren't written down anywhere. When a new browser vendor wants to enter the market, they just have to test malformed documents in various browsers (especially IE) and reverse-engineer their error handling. If they don't, then many pages won't display correctly (estimates place roughly 90% of pages on the net as being at least somewhat malformed).
So, HTML5 is attempting to discover and codify this error handling, so that browser developers can all standardize and greatly reduce the time and money required to display things consistently. As well, long in the future after HTML has died as a document format, historians may still want to read our documents, and having a completely defined parsing algorithm will greatly aid this.
The secondary goal of HTML5 is to develop the ability of the browser to be an application platform, via HTML, CSS, and Javascript. Many elements have been added directly to the language that are currently (in HTML4) Flash or JS-based hacks, such as <canvas>, <video>, and <audio>. Useful things such as Local Storage (a js-accessible browser-builtin sql database, for storing information beyond what cookies can hold), new input types such as date for which the browser can expose easy user interface (so that we don't have to use our js-based calendar date-pickers), and browser-supported form validation will make developing web applications much simpler for the developers, and make them much faster for the users (since many things will be supported natively, rather than hacked in via javascript).
HTML4 vs HTML5 
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