In the 1950's and 60's, customizing cars was a big thing. A normal car would be bought, new or used, and then customized. For example, the engine would be taken out and most or all of it replaced with chrome parts. The exhaust sytem may have had only one pipe and muffler, but it could have been modified to a dual system. We personalize something by adding our own ideas or items to it.
Lets use an apartment as an example.
The apartment may have two bedrooms, a livingroom, diningroom, kitchen and bathroom. We can't alter it when we rent it, but we can personalize it. We can use our own style furniture, we can decorate the walls with our own pictures or wall decorations. We may even be allowed to paint the walls the color we want. We just can't change or customize the apartment from its original layout.