Sometimes a subject has many words that modify or describe it. If you take away all the modifying or describing words and just keep the main subject (noun or pronoun), it is called the simple subject.

A simple subject is a subject that has just one noun or pronoun as the focus of the sentence. This means that only one noun or pronoun does the action, or connects, to the verb of the sentence.

For example:

The hungry fox darted across the yard.

Here, the complete subject is "the hungry fox." There are two more words like the and hungry that modify the main subject, which is the word fox. So, fox is the simple subject.

Similarly,

The old brown polka dot box was under the table.

Here, the complete subject is "the old brown polka dot box" while the main subject is just the word "box." There are many words like the, old, brown and polka dot that modify the main subject, which is the word box. So, box is the simple subject.

Simple Predicate

A predicate can also have many words. It also has a main part which is the simple predicate.

The simple predicate is the verbs or verbs that are connected to the subject.

In the example we just looked at,

The hungry fox darted across the yard.

Here, the simple predicate is just the verb darted instead of darted across the yard.

Similarly in the example,

The old brown polka dot box was under the table.

The simple predicate is just the verb was instead of was under the table.

Summary

Sometimes a subject has many words that modify or describe it. If you take away all the modifying or describing words and just keep the main subject (noun or pronoun), it is called the simple subject.
A simple subject is a subject that has just one noun or pronoun as the focus of the sentence.
A predicate can also have many words. But it has a main part which is the simple predicate.
The simple predicate is the verb or verbs that are connected to the subject.