If you vandalize something, you damage or destroy it. Graffiti can be art, but if you spray paint your initials on a marble statue, you vandalize it.
Vandalize has an ancient root: the Vandals were a Germanic group of people who famously sacked Rome in 455. Thanks to the terrible destruction they left in their wake, the word took on a meaning of "willful destroyer of what is beautiful." To vandalize is to deliberately damage something that doesn't belong to you. For some, it's a tradition to vandalize whole neighborhoods on the night before Halloween, strewing toilet paper in trees, smashing jack-o'-lanterns, and spray painting property. We recommend just trick-or-treating instead.