Every complete sentence contains two parts: a subject and a predicate. The subject is what (or whom) the sentence is about, while the predicate tells something about the subject.

A compound predicate is a predicate that includes more than one verb pertaining to the same subject.

An example is: Her Mistress and she walked slowly through the play party and admired the many punishments exhibited around the house.

Walked and admired being the verbs.