Poach basically kills an enemy and turns them into a piece of loot. I believe they still drop loot as well funny enough...

"Chains" in this instance is when you begin to kill the same type of enemies over and over again. Your first look at it was probably during the Yensa Sandsea section cause there are tons of similar enemies wandering the area. As you increase the chain in this instance, enemies start dropping multiples of common loot and even raise the chances they will drop rare items. Eventually, once you chain kill 60 -100 enemies, you can start getting minor HP/MP restores for your party. Later in the game, these kill chains will be very important if you want the ultimate items (like Tournesol) that can only be obtained in the Bazaar.