Cleave, a verb, has two very different meanings. It can describe cutting or splitting something apart with a sharp instrument, or — oddly enough — it can describe sticking to something like glue.
To cleave or not to cleave, that is the question. Cleave can refer to being in close contact, to staying really, really close to someone or something: "If you are walking in the pitch-black woods without a flashlight, you want to cleave to the person in front of you." On the other hand, it can mean to split apart with a sharp tool — which is not the action you want to happen while walking in the woods. We've seen that movie.