Because Office 365 is a subscription service, the familiar desktop applications get new features. Word is about to get a spelling and grammar checker that uses machine learning to understand your writing, and a Researcher tool for easier searching for facts and quotes.
PowerPoint has gained several new transitions, a Designer tool that comes up with new looks for your presentation (very much like Sway) and a way to summarise your presentation with Zoom. Excel has new functions and charts and shape recognition when you draw on-screen, plus many more connectors for getting data into Power Query, while Outlook lets you '@ mention' people in email the way you would on Facebook or Twitter.
But the changes also include removing some useful features. Changing the Save As options in Office 2016 has been particularly painful, and Office 365 no longer allows you to temporarily stream Office 2016 to a PC that you want to work on, if the Office Online versions don't have the features you need. Desktop Outlook is going to get the Focused Inbox that's so popular in Outlook for iOS and Android – but it will replace the Clutter feature in Exchange Online that files emails you're not likely to be interested in. Clutter worked in every client that you can read Exchange email in, including on older devices (especially Windows Phone 8.1), whereas Focused Inbox will only work in the latest versions of Outlook.
The enterprise Office 365 service is also where Microsoft tries out new features that will appear in the on-premise server products, like the new SharePoint 2016. Exchange Server 2016 is based on the latest version of Exchange Online, which has been available on Office 365 for some time (and you can buy some Exchange Online features to use with your own Exchange Server, like Exchange Online Protection spam and malware filtering).
SharePoint 2016 catches up with existing Office 365 features like chatting while you're collaborating on documents stored in OneDrive for Business, and will get newer features gradually. Improvements like the new document library experience, and the suggestions in the new iOS SharePoint app of what sites you should look at, are already showing up in SharePoint Online and will appear on premises once they've been tested in the cloud.
In the past, Skype for Business hasn't had the full unified communications features of the on-premise version because PABX integration is harder in the cloud, but Microsoft has been signing up partners like BT to offer voice services for Office 365, as well as creating cloud-only features like Skype for Business broadcast meetings for very large numbers of users (which will soon include real-time live translation and captions).