Can anyone please show some examples of sentence fragments?

A fragment is essentially a piece of a sentence.  A
complete sentence needs a subject, something that performs an action in the sentence,
and a verb, the action that is performed.

Here are some
sample fragments for you:

A piece of
cake

This is a fragment because there is no verb.  We do
not know what this piece of cake is doing.

Ran to the
corner.

In this fragment, there is no one running to the
corner.

Having a very bad
headache.

Here, we have a verb form and a noun, but this is
a fragment because we have no idea who has a bad headache or what the person with the
headache is doing about it.

One point I want to make here
is that it is not simply a question of having a noun or pronoun and a verb. If the noun
or pronoun is not doing anything, or if the verb is not giving the noun or pronoun some
action, you will still have a fragment.