Priority can be defined as "A player's 'right' to be able to activate his/her effect, ensuring its spot on Chain Link 1." Priority does not allow players to automatically activate and resolve effects without a chain; it simply assures a card's activation (not resolution), and guarantees a place on Chain Link 1. How the chain resolves is up to the players.
Priority tells you who can activate an effect at any certain point in the game. Note that cards never have priority'; it is the players who have priority. The Turn Player always starts with priority.
Player A has a face-up "D.D. Warrior Lady". He Sets a "Bottomless Trap Hole" and ends his turn.
Player B Special Summons "Chaos Sorcerer".
Player B, now being the turn player, says he wishes to retain his priority to activate the effect of "Chaos Sorcerer". "Chaos Sorcerer"'s Ignition Effect then activates, targeting "D.D. Warrior Lady". "Chaos Sorcerer"'s effect is now Chain Link 1. Player A then activates his "Bottomless Trap Hole", since the Special Summon of "Chaos Sorcerer" was the last action to have resolved on the field. "Bottomless Trap Hole" is now Chain Link 2.
source: http://yugioh.wikia.com/wiki/Priority
Priority tells you who can activate an effect at any certain point in the game. Note that cards never have priority'; it is the players who have priority. The Turn Player always starts with priority.
Player A has a face-up "D.D. Warrior Lady". He Sets a "Bottomless Trap Hole" and ends his turn.
Player B Special Summons "Chaos Sorcerer".
Player B, now being the turn player, says he wishes to retain his priority to activate the effect of "Chaos Sorcerer". "Chaos Sorcerer"'s Ignition Effect then activates, targeting "D.D. Warrior Lady". "Chaos Sorcerer"'s effect is now Chain Link 1. Player A then activates his "Bottomless Trap Hole", since the Special Summon of "Chaos Sorcerer" was the last action to have resolved on the field. "Bottomless Trap Hole" is now Chain Link 2.
source: http://yugioh.wikia.com/wiki/Priority