Key Grammatical Terms: Phrase, Clause, Sentence, Sentence Fragment

Phrase
A phrase is a single word or a collection of words that work together as a single part or unit. A phrase does not contain a subject and a verb and cannot convey a complete thought. 

Clause
A clause contains a subject and a verb and may or may not convey a complete thought.

Independent Clause
An independent clause is any clause that can stand alone as a sentence: It has a subject and a verb and expresses a complete thought.
I wrote a poem.

A sentence is an independent clause.

Dependent Clause
A dependent clause  is a group of words with a subject and a verb; however, a dependent clause does not express a complete thought and therefore cannot stand alone. Dependent clauses usually begin with  subordinating conjunctions (After, Although, As, As if, Because, Before, Even, Though, If, Since, That, Though, Unless, Until, When, Where, Whether, While, etc.) or relative pronouns introducing subordinate clauses (Who, Whom, Whose, Which, and That):

When she arrives
Because I am waiting for the bus
If you can work on Mondays

Whose stories are always scary
Where I went to high school
Whomever you like

Dependent clauses are sentence fragments. (A sentence fragment is a word, phrase, or clause that appears to be a sentence but lacks the proper grammatical structure. It may have a subject and a verb, but it lacks complete thought.) 

Subject

A subject is a word or word group that does an action.

Josie (subject) ran (verb) a marathon (object).

Who ran the marathon?  Who did the action of running? Josie.

Object

An object is a word or word group that receives the action of a verb.

Josie (subject) ran (verb) a marathon (object).

What did Josie run? She ran a marathon.

What received the action of running? The marathon is what was run.