I'm currently in 10 DNA Circles - the lowest circle has 7 members and the top circle has 11 members. A couple of the circles duplicate information I already know (i.e. people I have contacted or they have the same people in them) and all of my Circles are based on my paternal line (I unfortunately have no DNA circles for my maternal line).
The main area that the circles work is to add all those with the same ancestors in their public trees into a circle - it can add people to the circle who are linked to other members of the circle even if they don't share DNA with you - thus this can add information or confirm information about people you have in your tree if you need it.
For example, the DNA Circle for my 4x great grandfather has 11 members. Five of those members are from my own family - and it lists their position - i.e. for me it states that I am "4th great granddaughter". It then shows links to four other family groups, only three of which I/my family group has DNA links to, for each DNA match, it gives a position like the one it offers for me (2nd/3rd/4th grandchild) - it groups each of these links into family groups particularly if there are people who have more than one member of their family having had their DNA tested.
It also offers a compiled blurb on the individual to which you are all related - unfortunately this uses as many ancestry trees as the person is in across Ancestry and thus is rife with errors.
One of my other circles is for a different 4th Great grandfather, and I find his "blurb" amusing every time I read it - the information was compiled from 58 family trees:
When James Henry B-- was born in 1812, in Portsea, Hampshire, England, his father, Henry, was 24 and his mother, Mary, was 24. He married Sarah H-- (1) and they had four children together. He then married Sarah H-- (2) and they had 16 children together. He died in 1883, in South Australia, Australia, at the age of 71, and was buried in Adelaide, South Australia, Australia. (and that is MUCH more accurate than the first time this DNA circle popped up. For a few of them it has them marrying and having children with five different people because the names aren't the same across every tree - in this case, his birth date & place, death date & place and parents names are correct)
The second marriage to the second "Sarah H" is completely incorrect; he had 12 children with his only wife (the first Sarah H listed), and the compiled information includes erroneous entries including census facts for 1851, 1861 and 1871 (the family were in Australia by 1840); an emigration for 1834 to another state in Australia (one of his children was born in Portsea in 1838 - I have their birth register); an arrival in 1849 in yet another state (he only lived in one state in Australia where he was considered a pioneer).
I find it useful for the collation of those people who share ancestors with me but at this point, considering the errors which it contains due to the nature of public trees it isn't particularly useful for much more. Plus, of course, it doesn't include anyone with a private tree. Most of the people in the Circles I already knew about because they will pop up with a "leaf" hint match - and I have more of those (18 hints) than I have DNA Circles - I think there has to be a certain number of people before a DNA Circle will be created.
My DNA Circles are for - 3 pairs of 4x great grandparents (1 circle for husband and 1 circle for the wife); a 2nd great grandfather (Grandson of one of the pairs of 4x great grandparents); a 5th great grandmother (mother to one of the 4th great grandparents in the pairs); 3rd great grandfather (descended from the 5th great grandmother), and an unrelated 3rd great grandmother. In total three branches of my paternal line are covered by a circle (or up to four different circles).
My mother did have a DNA Circle - added in for someone my mother had DNA links to, but wasn't in my tree - that was removed after Ancestry changed the way it added DNA Circles. My mother instead has 2 "New Ancestor Discoveries" (those were the people she originally was put into a Circle with) - people that she has DNA links to, who are not in my family tree. For one of them, there are 30 members of the circle and my mother has DNA links to three of the members and the other has 24 members and my mother has DNA matches to 5 of them. Unfortunately I have had no luck in adding either into my family tree as of yet - almost like a different version of a brick wall!