With a New generation of Pokemon comes a number of new mechanics involved in all aspects of Battle, as well as outside of such. There are even some mechanics that have been altered since generations past.

New Mechanics
#1: Z-Moves a New way of powering regular Moves. Z-Moves can be used on Status Moves.
#2: Male Parents can pass down same Poke Ball if bred with Ditto.
#3: SOS Battles can be used for Shiny Hunting, EV Training and Finding Pokemon.
#4: Ability to add Pokemon immediately after capture, even if Party is full.
#5: Ability to heal Pokemon with Pokemon Refresh instead of using Items.
#6: Ability to improve a Pokemon's IVs through Hyper Training
#7: New Evolution Moves created where Pokemon learn upon evolving.

Altered Mechanics
#1: Burn Status Condition now removes 1/16th of HP instead of 1/8th.
#2: Paralysis Status Condition now cuts Speed in half instead of two-thirds.
#3: Many Moves have been altered.
#4: Many Pokemon Stats have been altered.
#5: Many abilities have been altered.
#6: Turn order has been Altered for Mega Evolutions.