Its owner will control the creature, and it will remain on the battlefield even if you leave the game (if you don't own it)
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(I always imagine it like being what youd get if chess had certain edge cases where rooks could fly, bishops could teleport, or for a second, pawns were driving tanks.) Since the game is built around several thousand collectible cards, and almost every card has some additional unique ability to it one way or the other, it creates an endlessly manipulable, constantly surprising experience
answering the few cards that can disrupt these decks will give you a huge edge, and you also have game against various strategies that attempt to go way over the top
You can destroy any creature with a mana value of 2 or less, and together with fetch lands you can remove any creature with a MV up to 4