Every subject is built around one noun or pronoun (or more) that, when stripped of all the words that modify it, is known as the simple subject. Consider the following example:

A piece of pepperoni pizza would satisfy his hunger.

The subject is built around the noun "piece," with the other words of the subject -- "a" and "of pepperoni pizza" -- modifying the noun. "Piece" is the simple subject.

Likewise, a predicate has at its centre a simple predicate, which is always the verb or verbs that link up with the subject. In the example we just considered, the simple predicate is "would satisfy" -- in other words, the verb of the sentence.

A sentence may have a compound subject -- a simple subject consisting of more than one noun or pronoun -- as in these examples:

Team pennants, rock posters and family photographs covered the boy's bedroom walls.

Her uncle and she walked slowly through the Inuit art gallery and admired the powerful sculptures exhibited there.

The second sentence above features a compound predicate, a predicate that includes more than one verb pertaining to the same subject (in this case, "walked" and "admired").