To wreak is to cause something to happen, usually with a terrible consequence. You can make mischief, cause problems, or inflict pain, but to wreak damage suggests a deeper level of destruction.
Wreak stems from the Old English wrecan, meaning "to avenge." Its current meaning, that of causing something to happen — usually with dire consequences — came about in the 19th century. The word is a transitive verb, often paired with the equally intense havoc, meaning "devastation."