What is priority?
Priority is a "right" each player has during a duel. What are these right? Well they mostly depend on who's turn it is. Although this has been old news, Priority lately has been used for monsters with Ignition Effects.
I want to talk to you about what that priority is.
Priority - Ignition Effect (NO LONGER EFFECTIVE IN THE CURRENT GAME!!!)
During the Player's turn, when he/she summons a monster with an Ignition Effect successfully, he/she can use it's effect (if possible) before the opposing Player, who is waiting, can respond.
Player A has Lyla, Lightsworn Sorcerer in his/her hand.
Player B has Bottomless Trap Hole facedown on the field.
If Player A summons Lyla, Lightsworn Sorcerer and it is successful, he/she can "call" priority and use Lyla, Lightsworn Sorcerer's effect and target Player B's facedown card. Now, Player B has a choice whether or no he/she wants to respond to the summon of Lyla, Lightsworn Sorcerer.
Nowadays, If Player A summons Lyla, Lightsworn Sorcerer, he/she must ask Player B if he/she has a response to the summon. Player B can respond with Bottomless Trap Hole and destroy Lyla, Lightsworn Sorcerer and banish it and Player A cannot use Lyla, Lightsworn Sorcerer's effect.
Now for what priority rights really are.
Priority - Player's Turn - Player Priority
During your turn you can
-Main Phase 1/2-
*Attempt 1 Normal Summon/Set if you have not during the turn.
*Special Summon as many monsters that you are capable
*Set or Activate any Spells/Traps that have the correct activation timing.
*Activate any Effects that can be activated
*Declare any and all attacks with your monster(s), if possible
*Activate and chain effects that are applicable at this time
Priority - "Waiting" Turn -
Not much can happen during except responses when the player decides to pass priority. The player waiting cannot activate cards without the player passing priority.
Priority - Chains
If 2 or more effects are activated simultaneously, the effects of the current Turn player get's its effects first, then they opponent's effects.
Passing priority is a term used to allow the Player waiting to respond to an action done by the Player's turn. A player also passes priority when he/she ends a phase.
Lemme try to rephrase this one point at a time.
Waiting Turn - Phase Priority
*The player waiting must wait for his/her opponent to end a phase before declaring a response.
Player A has a Legendary Six Samurai - Shi En.
Player B has Formula Synchron and Wind Up Shark
It is Player A's Main Phase.
Suppose Player A chooses not to make a move during Main Phase 1 and moves on to Battle Phase.
Player A must declare "entering Battle Phase" or "ending Main Phase 1" to simulate that he/she ends priority for Player B to use Formula Synchron's Effect. Player B cannot use Formula Synchron's effect without responding to Player A's actions. If Player B chooses to respond to Player A ending a phase, Player A can return to the phase he/she was ending and continue it if he/she wants.
Priority - Response
The player waiting gets the priority to respond to an action that the Turn Player made, before the Turn player can respond to it.
Player A has 2 Jurrac Guaiba and 1 Jurrac Gallim on the Field, Jurrac Meteor in the Extra Deck, and Different Dimension Transporter set (supposing 1 turn has passed)
Player B has Starlight Road and 2 other cards on the field.
If Player A uses the 2 Jurrac Guaiba and 1 Jurrac Gallim for the Synchro Summon of Jurrac Meteor, Jurrace Meteor will activate it's effect, Player A cannot activate Different Dimension Transporter targetting Jurrac Meteor without asking Player B for a response to the effect.
If the situation is like this
Player A has Wind-Up Rat and Wind-Up Shark in Hand
Player B has Effect Veiler in his/her Hand.
If Player A Normal Summons Wind-Up Rat, both Wind-Up Shark and Effect Veiler activation timing are the same, since it is simultaneous and it is Player A's turn, he/she is able to activate Wind-Up Shark's effect as Chain Link 1 as Effect Veiler is Chain Link 2.