The phrase "to unlock this trophy" means that you have achieved a particular accomplishment or completed a specific task required to earn a reward or recognition. Full definition
Who wants to pay the price of a little game to just play offline with bots and unlock trophies in vain and not in the way they were meant to be gotten? (blog.us.playstation.com)
Anyone who can unlock the trophy for completing the game with five or fewer deaths is officially better than us. (ps3attitude.com)
My only question would be, existing games you've already unlocked things in, say Uncharted, will the patch automatically allocate unlocked trophies or would you have to do it again? (blog.us.playstation.com)