The verb is the word that tells what you can do — that is, an action word.
The sentence "the girl who ate all the cake" is a fragment because it does not express a complete thought. A complete sentence should have both a subject and a predicate and convey a complete idea. In this case, there is a subject ("the girl who ate all the cake"), but there is no verb or predicate to provide a complete thought or action. To fix this fragment, you could add a verb or predicate to complete the sentence, such as "The girl who ate all the cake was happy" or "I saw the girl who ate all the cake." Adding a complete verb and providing more context would transform the fragment into a proper sentence.