One of the handy features of Azure AD Premium was the ability to install a small program on each workstation and then have it report on cloud based applications used. All the data was collected by Azure and then reported in a handy dashboard.
That way you could see what cloud based applications were in use, how much data was flowing through them and whether they were being used outside the Azure AD Single Sign On Web Portal.
A good example I have seen is where cloud app discovery uncovered the fact that a number of employees were sharing large amounts of corporate information using Dropbox which had been banned from the workplace. Cloud Discovery allowed these users to be identified along the times sharing was taking place. The business could then take appropriate action.
According to this post from Microsoft:
Cloud App discovery is a new feature, amongst others, coming to Office 365. To quote:
Office 365 cloud app discovery gives you the ability to understand which other cloud services your users are connecting to. From the Office 365 admin portal, you can view a dashboard on network activity. For example, you can see where users are storing and collaborating on documents and how much data is being uploaded to apps or services outside of Office 365.
Not quite sure how exactly it works but I expect it will be a slightly cut down version of what is available in Azure AD Premium, like many other enhanced features of Office 365 are.
There are also some other great security enhancements announced in that blog post so check it and be ready for the new features arriving in an Office 365 near you soon!