What isn't clear is whether this is something that will be iCloud-like in its approach or something completely different. Apple could be giving developers two separate sets of APIs for storage: one for iCloud, which was mentioned specifically during the keynote, and one for WebDAV on Lion Server. The more logical approach would be to use a single cloud storage API in multiple ways.
Lion Server aside, one implication is that iOS file sharing/storage (iCloud or not) is based on WebDAV. That wouldn't be completely surprising. Apple's current iDisk feature is based on WebDAV. In fact, that's how you connect to it from a PC that doesn't have Apple's Mobile Me control panel applet installed. Apple has also showed preferences for customized uses of WebDAV and WebDAV-derived services like CalDAV and CardDAV over the past few years in iOS, Mac OS X and Mac OS X Server.
If Apple is basing over-the-air file storage and sharing in iOS 5 on WebDAV under Lion Server, it's quite possible that that service could be replicated with other WebDAV servers running on other platforms.
What would this look like on an iOS device?
Over the air
Whether it functions exactly like iCloud or not, Apple is clearly planning to allow-over-the air access to files as part of iOS 5 and Lion Server. It's far to early to tell with any degree of certainty exactly what this will look like, but given Jobs' comments about ending the need to access the file system it won't likely involve any type of file browser.
That means any on-device or over-the-air file storage is probably going to be app-specific; Users will likely have access to files on their device, files associated with their iCloud account, and files on any other Lion Server/WebDAV "file servers" they have access to.
My guess would be that there will be another option added to the Accounts section of the Mail, Contacts, Calendars area of the iOS Settings app. Right now, if you add an account and select Other as the account type, you can add a Mail, LDAP, CardDAV, or CalDAV account (or a .ics calendar URL). It isn't hard to imagine that list including a WebDAV account, perhaps named something like File Sharing.
With one or more such accounts enabled, users would likely see app-specific document stores for each account in any app that supports off-device file storage. It isn't clear whether these document stores would have a cloud-sync capability, though I'd lay odds that they would involve some form of permissions -- most likely those configured on the WebDAV server.
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