The Office 365 Groups are Microsoft's new innovation, and they're pushing for them hard. Right now, if you try to create a distribution group, it'll try to push you toward creating an Office 365 Group (referring to it as creating a group in Outlook; an Office 365 Group and a Group in Outlook are the same thing, as an Office 365 Group can be created by a user, using Outlook as the interface). Create and edit them in much the same way as you do other groups; the options aren't identical, but they're close.
The owner defaults to the account you're logged in as, but you can change it by browsing to a different user.
For all groups, removing them is as simple as clicking on the group name in the main Groups window ...
