A cleft in a rock or in the ground is a narrow opening in it.

A cleft in someone's chin is a line down the middle of it.

If someone has a cleft chin, they have a cleft in their chin.

If you say that a person or organization is in a cleft stick, you mean that they are in a difficult situation which will bring them problems and harm whatever they decide to do.

Cleft is a past participle of cleave.