A compound subject is two or more simple subjects combined by a conjunction (and, but, or). "Ann went to the market:" Ann is the simple subject. "Ann and Peter went to the market:" Ann and Peter is a compound subject.
A sentence has a compound subject when more than one person or thing is doing the action. In the sentence: Mike and Tina went to the movies. "Mike" and "Tina" both went to the movies, so they are both the subject of the sentence.
