Something that's specially designed for you is personalized. A personalized coffee mug might have a photo of your cat on it, and a personalized backpack could be embroidered with your initials.
Personalized items are made to one person's exact specifications or marked in some way to show ownership. A personalized spa experience might include selecting a special scent for your foot soak or a particular color for your nail polish. A personalized dog bed has your dog's name on it. Think of it this way: anything that's personalized is made personal or aimed at one specific person (or dog).