A sentence fragment is a piece of the whole.
You can't drop a plate on the ground, pick up a shard of it and say "Hey, look: a plate!" Same rules apply here. Your typical sentence fragment is a group of words that makes up only part of a sentence. It's an incomplete thought. Sentence fragments often leave the reader scratching his or her head, wondering what's missing.
So what is missing?
A sentence fragment may be missing a subject, a verb, an object, or any combination of the three.
Finished her potato clock for the Science Fair.
This sentence is missing its subject. Who finished building a clock out of a potato?
The hyperactive iguana.
This sentence is missing its verb. What did the hyperactive iguana do? We're dying to know. Also, depending on the verb, the sentence in question could be missing an object, like in the following:
The hyperactive iguana devoured.
This is a little different from saying "The hyperactive iguana ate." That sentence is totally fine. So why is the above sentence wrong? Well...we don't really have an explanation, Shmooper. That's just the way language is. Some verbs absolutely need an object. Other verbs like this are: send, message, plant, etc.
A package to Louie.
This sentence is missing its subject and its verb. All we know is that a package to Louie exists. It sounds a little terrifying.