What sort of figurative language is used in this sentence: "cautiously, we entered the yawning cave"?

This is an example of personification.

Figurative language is language that is not meant to be taken literally.  It is colorful and creative, and is used to create a picture in the reader’s mind.  Authors can use figurative language to describe a setting or for characterization.

Your example uses personification to describe the cave.  Personification is a type of figurative language in which something that is not human is described as human or given human characteristics. When the cave is described as yawning, it is personification because yawning is something that a human being does.  Describing the cave as yawning means that the entrance to the cave is very big, and possibly scary.

Personification like this helps to enhance the description of the setting and also can create suspense. When you describe a cave as “yawning” it sounds like it is a monster or something. The cave is big, and it is unknown. This is the beauty of figurative language.