The term "compound subject" is used to refer to a type of sentence structure in which more than one person or thing is performing an action. The subject of a sentence is the "doer" of the sentence, or the person or thing who is acting. The word "compound" refers to something that is made up of more than one part. A compound subject is therefore more than one person or thing combined to perform an action. When using such a structure, the verb conjugation may change as a result of the presence of more than one actor or doer.
Here is an example of a sentence with a single subject:
John went to the store.
In this sentence, the subject is John; the verb is went. There is only one person or thing doing the action; in this case, that single person is John. In order to form a compound subject, another person or thing needs to be acting in conjunction with John. Here is an example of a sentence that features a compound subject:
John and Mary went to the store together.
In this sentence, there are two actors or doers--John and Mary. Together, they went. Went, in this case, is the verb, or action. Both subjects are performing the same action, which means, therefore, both subjects are assigned to the same verb. Notice, too, that the two subjects are joined by a conjunction, which in this case is the word "and." Other conjunctions can be used to change the meaning of that sentence. For example:
John or Mary went to the store.
Notice that the use of the conjunction "or" changes the meaning of the sentence, though both subjects are still assigned to the same verb.
It is possible to have two subjects in a sentence without creating a compound subject. This sentence, for example, features two distinct subjects, but also two distinct verbs:
John went to the store, but Mary stayed home.
This is a compound sentence, but there is no compound subject here. In the first part of the sentence, the subject is John; he went, which is the verb. In the second part of the sentence, the subject is Mary. She stayed, which is the verb. If two subjects exist in a sentence but there is more than one identifiable verb — one verb for each subject — then the sentence may not have a compound subject but instead may be a compound sentence.