Controller

Source: Yugioh Wikia

The Controller of a card is usually the one who has it on their side of the field. The controller can change the Battle position of monsters they control If the monster is face-down then only the controller of the monster can see the card. Your opponent cannot see the face-down card unless if the monster is targeted to reveal the monster or they are the new controller. The effect of a card is applied normally if control is changed.

Example:

Player 1 Sets "| Dharc the Dark Charmer".

Player 2 Summons "| Destiny Hero - Defender".

Player 1 Flip Summons "Dharc", and uses his/her ability to take control of "Defender" and changes "Defender" into Defense Position.

Player 2 draws a card via "Defender's" effect.

Even though Player 2 owns "Destiny Hero - Defender", "Defender" is on Player 1's side of the field. Player 2 is Player 1's opponent, so Player 2 draws the card.

If "Defender" were to be removed from the field, it would be moved to Player 2's Deck, Graveyard, etc.

Cards such as "| Reshef the Dark Being", "| Creature Swap" and "| Enemy Controller" are capable of switching the controller of monsters. Should said monsters be destroyed, they are sent to the owner's Graveyard. Some monsters, such as "| Mataza the Zapper]" and "| Blindly Loyal Goblin" are immune to such effects.