The two main parts of every sentence and every clause are subject and predicate.

The subject is what a speaker is talking about.

The main word in the subject will be a noun or a pronoun.
This main word is the SIMPLE SUBJECT.
The subject word with all the words that describe it is called the COMPLETE SUBJECT

The subject may be a single word:

Cats are beautiful. (simple subject)
He won the lottery. (simple subject)

The subject may contain several words:

The tall, red tower stood beside the sea. (complete subject) The simple subject in this sentence is tower.

The subject may contain phrases as well as single words:

That good-looking boy in the blue shirt watches out for the younger children on the playground. (complete subject) The simple subject is boy.

The subject of a sentence usually comes before the predicate, but sometimes it comes after it.  When the subject comes after the predicate, it is called a delayed subject. Here are some examples:

There were three kittens on the porch. (complete subject)
Once upon a time lived a horse with wings. (complete subject)

Delayed subjects are explained in more detail elsewhere on the site.