The first big feature is the unified inbox. Finally, it will be possible to read all of your unread messages in one "pane" without having to navigate forwards/backwards between the many accounts on your device. As someone with 5 email accounts that I regularly check, this is a huge win.
Multiple Exchange accounts means I can finally have both my work email (Exchange) and my personal email (Gmail) take advantage of Push functionality. Previously users were limited to using one Exchange account and unlimited IMAP accounts. This limitation has been removed. And there was much rejoicing. Additionally, fast inbox switching means it is easy and quick to focus in on a single mail account.
Threaded messaging is another feature that has been asked for by many. If you have ever used Gmail's web client, then you are familiar with how this works. Essentially, messages that pertain to a single "chain" of emails (based on subject line) are grouped together. This greatly reduces a cluttered-feeling inbox and I recommend checking it out on your Mac using Mail.app by enabling the Threaded Messaging view.
Now that the iPhone and iPad have become / are becoming huge winners in the productivity space, this next feature is going to be a welcome addition as well. The ability to open attachments with third-party apps is a great idea that I've only recently begun to feel as a regular need. I think this really helps to push the iPad towards true laptop-replacement status.
That's all we've got so far on the new features in Mail coming with iPhone OS 4.0. Stay tuned as we continue to cover this monumental update to Apple's mobile operating platform.