A Crucial Item

The Z-Ring Is A Bracelet With a Crystal That Fits In The Hole Called  A Z-Crystal. There is no Backstory on it except they are used to perform Z Moves. There are Ananan Z Rings and Crystals Including: Pumjaxinum, Hexinum, Diginum, Etc.

A Firium Z only turns into A Pumjaxinum if you have a Pumber and a strong relationship. With this Z crystal, You can perform the Z-Move, Erupting Volcanic Stomp, That can summon lava and magma out of the floor. A Hexinum Z is a Z-Crystal That Only Works If You Have A Zygarde Full Form. Using this Z-Crystal, You can perform the Z move, Digital Overdrive. A Diginum Z also works If You Have A Zygarde Full Form And A Hexinum Z. It Turns Into A Diginum Z When Zygarde Is Attacked And Gets Hurt A Lot.

In the anime, All of these people have Z- Rings,

Ash

Kukui (As shown with Tapu Koko)

Alima

Mallow

Lillie

Kiawe

Sophocles

Lana

In The New Region, These are the the people Owning Them:

Jay (Team Vine Leader)

Jax

Prof. Acacia (League)

Fin

Ash (Dual Z-Move)

Etc.

There are many more to see so check Google for the rest.