A pun is its own reword.

I'm shamelessly plagiarizing these from the pun site because they made me laugh.

Show me a piano falling down a mineshaft and I'll show you A-flat minor.
I wondered why the baseball was getting bigger. Then it hit me.
To write with a broken pencil is pointless.
If you don't pay your exorcist you get repossessed.
A cardboard belt would be a waist of paper.
What's the definition of a will? (It's a dead giveaway).
There was once a cross-eyed teacher who couldn't control his pupils.
He wears glasses during math because it improves divison.
There was a ghost at the hotel, so they called for an inn spectre
She was only a whisky maker but he loved her still.
Atheism is a non-prophet organization.

Homographic puns make use of multiple meanings from a single spelling. These are also referred to as "antanaclasis". Homophonic puns use like sounds but with different spellings and meanings. This is also referred to as polyptoton.

My name is Dave, and I'm addicted to puns.