A Z-ring and a Z-Crystal (of a certain type) are used to use Z-moves, which is essentially a one-time use nuke button. It is often used on certain Pokemon as a lure or to break thru walls and OHKO them. Some example of Z-move users are Heatran with Z-Solarbeam to lure in Water types or Lando-T with Z-Stone Edge to majorly dent Skarmory, Celesteela and other Lando-Ts. Z-moves also activate with status moves, giving them a boost while using the move, for example Z-Hypnosis boosts the users Speed by one AND can put the foe to sleep while Z-Conversion boosts all the Pokemon's stats (like Ancientpower) and changes the type to the move in the first slot like normal.
Alolan forms are regional variants of older (gen 1) Pokemon which are found in, Alola. They change up the design, typing, and movepool of the Pokemon and often times are better than their regular counterpart. The two most relevant Alolan forms in OU are Alolan Muk & Marowak, Muk has a Dark type added onto its Poison giving only one weakness and gets both Pursuit and Knock Off while Alolan Marowak has a completely different typing of Ghost/Fire allowing it to counter a lot of the metagame with Thick Club boosted attacks. While the Ultra Beasts are just legendaries from some next dimension that seem to have bipolar stat distribution.
As for the meta, it is generally focused on the four new legendaries, being the Tapu quadrant and their abilities that summon the terrains (remember them from gen 6?). Tapu Koko summons Electric Terrain upon switchin and generally acts as a fast and hard hitting pivot with Volt Switch. Tapu Lele summons the new Psychic Terrain which prevents priority moves from being used and boosts Psychic moves by 1.5x, hitting really hard. Tapu Bulu summons Grassy Terrain healing any grounded foes while hitting the hardest of Wood Hammers. While Tapu Fini is shrugs off status with Misty Terrain and eats hits like nothing. Some of the Ultra Beasts are common in OU right now, with Pheromosa currently being suspect tested (and likely getting banned) for its Deoxys-A like stat distributon and Celesteela being a Skarmory with Leech Seed and Heavy Slam dunking most of the tier. A lot of the older mons are still good, such as Lando-T, Heatran, and Megagross (who works exceptionally well with Lele), while some Ubers are back in OU like Hoopa-U, Greninja, and Mega Mawile. Hope this helps.
