In the sentence "The children are sleeping," the verb string "are sleeping" is an example of a simple predicate. A predicate describes the action performed by the subject of a sentence. In its simplest form, a predicate consists of only a verb, a compound verb or a verb string.
The subject of a sentence describes who or what is the focal point. The action is received by the direct object. In the sentence, "The store owner brought donuts for the staff," the action is performed by the store owner. The verb "brought" is the simple predicate, and "donuts" is the direct object receiving the action. A simple predicate containing a compound verb consists of multiple actions modifying the same subject and direct object. This sentence is an example: "The dog barked and howled at the mailman."