Technically this isn't a new feature, as it's been built into Nougat, but only for Android TV. With Oreo, though, it's available for every device out there, phones and tablets included. As you'd imagine, it works best with video playback and video chat, but certain apps not focused on videos support it too (Google Maps, for example).
To go into Picture-in-Picture (PiP) mode with a video, you start playing it in fullscreen and then hit the home button. Once you've done that, the video is relegated to a small, moveable window that is displayed on top of everything else. You can then keep watching said video while going about doing other things on your phone or tablet, and when you've had enough you simply drag the window down to dismiss it. In case you were wondering - yes, you can use split-screen multitasking and PiP at the same time.
You're probably expecting YouTube to be the prime candidate for PiP usage, but there's a huge caveat. You can only put videos in PiP mode from the YouTube app if you subscribe to YouTube Red, the premium ad-free tier that is still only available in a grand total of five countries. If you don't pay for Red, you simply won't get PiP functionality inside the YouTube app at all. A workaround involving the YouTube website in Chrome used to work but doesn't anymore. Speaking of which, PiP in Chrome is compatible in theory with any video on any website other than YouTube, but remember to go fullscreen before hitting the home button.
In Google Maps, once you have entered navigation mode, you can hit the home button and the app's UI will switch to a PiP window, still displaying information about your next turn and ETA, while showing as much of the map as possible in such a small space.
If you've ever used a web browser on a computer you probably understand the concept of autofilling online forms - with usernames and passwords, yes, but also other information (addresses, credit card numbers, and so on). With Android 8.0, Google is bringing such possibilities to the OS level. So in Oreo, you don't just get autofill abilities in Chrome - you can in fact use autofill for apps.
For example, let's say you've stored your Twitter username and password in Chrome on your desktop (and have syncing enabled). Then you install the Twitter app on your Android phone. When it comes time to sign into that, Google's autofill service will conveniently ask you if you want it to use the already stored username and password. If so, it will do its magic - and you won't have to type in anything. Similarly, when you log into a new app on your Android device you'll be asked if those details should be saved for later use. Remember - this happens inside any app, not just the web browser of your choice.
Since this is an API, third parties will be able to tap into it. So if you don't want your usernames and passwords stored by Google, you'll be able to choose a service such as LastPass for the same purpose.
For quite a while, the default emoji set in Android has had a weird blob-like format, unlike any other mainstream emoji design. Some loved that for its uniqueness, others hated it for how different it was, but none of that matters now because the blob emoji have been killed by Google in Oreo.
The entire emoji stack has undergone a redesign, with circle-based faces. Although they still don't look identical to what other companies are doing, Android emoji are now a lot more similar to other designs. In addition to the redesign, over 60 entirely new emoji have been added to Android 8.0.
While the new look does help with usability somewhat, the emoji situation overall is still a mess since there isn't a standard design across apps and platforms - even on Android, some chat apps use their own icons. Not to mention that quite a few Android device makers have a propensity for coming up with their own designs that replace the default set. And of course other mobile operating systems each have their own interpretations.