Groups
A shortcut for sharing, and deliberately nothing more.
A group is a name and the people in it. Flat, Parents, Weekend crew.
Share a list with a group and everybody in it reaches the list. Add somebody to the group later and they reach it too, without anybody going back through the lists to find what they are missing.
Making one
Settings → Groups → New group. Name it, and pick who is in it while you are there — a group with nobody in it does nothing, so there is no reason to make one and then go looking for the edit button.
What a group is not
It has no lists of its own, no settings, and no permissions beyond who is in it. It never becomes a hierarchy to maintain, because a household todo that needs an org chart has stopped being a household todo.
That is why the groups page shows you the lists a group reaches. What a group reaches is the whole of what a group does.
Who can make them
Admins. A member can share a list with a group that exists, but making and changing groups is instance administration.