When a writer capitalizes and punctuates a piece of a sentence as if it were a complete sentence, that’s a sentence fragment. The most common types of fragment are the following:
 
Verbal phrase punctuated like a sentence
Here are some examples of common mistakes:

• Connecting the two pieces.
• To find where the Beatles lived.
• Therefore accomplishing his third goal.
• Giving you reenactments of her past life.

To correct this type, add a subject and verb to the beginning of the phrase or add a verb plus adjective or noun.

• Connecting the two pieces, he figured out the puzzle.
• The couple looked online to find where the Beatles lived.
• Therefore accomplishing his third goal, Timothy graduated medical school with honors.
• Sheila was giving you reenactments of her past life.

Dependent clause of a complex sentence (the half of the sentence which begins with the connecting word.)
Here are some examples of common mistakes:

• Because she got paid today.
• A man who is complex to some.
• Which are shiny and dappled.
• Until someone releases them with a bite.

To correct this type, connect the dependent clause to the sentence before or after it (whichever makes sense).

• Because she got paid today, Julie bought groceries.
• A man who is complex to some, my father is open and clear with me.
• The horses, which are shiny and dappled, played in the field.
• The worms are stuck on the hook until someone releases them with a bite.

http://owl.ccd.edu/writ_resources/handouts/Frag_Exp.html