If a friend gives you a gift that only you will like, that gift is individualized — made especially to fit your personality and no one else’s. What a thoughtful friend!
Inside individualized is the word individual. So, just like a unique individual, when something is individualized — it is one-of-a-kind. A parent might cook you an individualized meal of your favorite foods, and at a carnival you can get an individualized cap with your name printed on it. A synonym is personalized, and it takes personal knowledge of a person to give them anything individualized.