To customize something is to make it exactly how you want it. If you put stickers all over your plain old notebook, you customize it.
If you see the word customer in customize, you’re onto something — to customize is to make something to a customer’s specifications. When clothes are customized — or tailored — they’re made with you in mind, specifically. A customized suit should fit perfectly. If you customize your car, it could be bright pink with eyelashes on the headlights. Or not.