A simple sentence, also called an independent clause, contains a subject and a verb, and it expresses a complete thought.

A. Some students like to study in the mornings.

b. Juan and Robert play soccer with some friends in the stadium

c. Alicia goes to the Library and studies syntax everyday :)

The three examples above are all simple sentences. Note that sentence B contains a compound subject, and sentence C contains a compound verb. Simple sentences, therefore, contain a subject and verb and express a complete thought, but they can also contain a compound subjects or verbs.