Depending on how developers set up the app you should be able to pick where and (within limits) how your offline data are stored.
HTML5 specs require that the User Agent not delete data without the user's say-so, so in general your documents are safe. Server-based apps can be set to override that and copy over or delete older data, however.
OK, I lied. There is a difference between local and Web storage.
Mainly it's that documents stored online have to be stored in a beefier database -- usually a Web SQL thing -- rather than within the browser itself.
App developers can write to those fairly easily to do two-way data synchronization or downloads, though, so from a user point of view there's not much difference except for which you can access when you're not connected.
OK, there's one more type of offline storage in HTML5, too. App caching.
Like prefetch in Windows, Application Caching is supposed to make applications run faster by downloading the software itself into a chunk of memory on your computer and then saving it to a separate section of your offline storage cache.
If the cache is for a game site that you revisit, the Java code, CSS, icons, images, sounds and other data that's a part of the game would load immediately because they're sitting on your hard drive and don't have to download.
Most browsers can do that now, but the caches into which most of that data are stored can be overwritten so you have the Java but not the CSS, the CSS but not the sounds or settings, which either confuses the software so it crashes or forces you to download the whole thing again.
When will it be available
It's available now, mostly.
Analysts said HTML5 will start out in pretty much the same niche as Flash -- doing games and light aniimation or coding of local apps. It is capable of supporting much more powerful code, but won't get into serious transactional or other highly secure, critical business applications for another couple of years.
There are already plenty of games and video available for playback using HTML5. More than half of all Web video can be replayed using HTML5, according to a study by MeFeedia, compared to 10 percent in January -- an increase analysts peg to high sales of the HTML5-using iPad.