The page on Kuriyama Mirai on Kyoukai no Kanata Wiki says she uses her ring to activate her ability.
From the show, I got the feeling the ring was something that kept some of her powers on check, rather than an activator.
I don't recall any explanation of how the ring works during the series.
Whichever the case may be, how exactly does the ring help her control/activate her ability?
Does the ring possess some kind of magic? Or is it some kind of psychological power it exerts over Mirai?
This answer only applies to the TV series proper. Additional information is given in Mirai-hen; see Amir's answer.
There isn't really much to be said about the exact function of her ring. It isn't discussed in the novel (though she is shown wearing the ring, cf. p004-005 of LN 1), so the best I have as far as a textual citation is this magazine scan (SFW image; NSFW site), which reads:
自分の血を剣に変えて戦う未来。普段は包帯と小指の指輪でその能力を抑えている
[...] For the most part, she wears a bandage as well as a ring on her little finger in order to keep her powers in check.
There isn't really any verbalized explanation of how the ring works in the show either - the best we can do is infer its function from its depiction in the show.
So, basically, it's probably just what you thought it was - a power limiter of sorts.
This is a late answer, but in the sequel movie "Mirai-hen" it was revealed that Akihito's mother made the ring from Mirai's mother's body after Mirai's mother died. Mirai's mother said she would supress Mirai's powers and protect everything that she held dear.
From the events in the anime, it can be inferred that the ring is in fact an object to keep her powers in check. The ring was a gift from the family that took her in, and she accidentally killed one of the daughters in said family. The ring serves as a reminder just how dangerous her abilities can be, and the mistake she had made. In the anime, Mirai's blood becomes more acidic whenever the ring is taken off. This can be seen when she gets into more serious fights. So, technically speaking, the ring helps her keep that acidity away from hurting her friends because she is reminded of what she did to the family.
