'Pun' is a play on words ( using words that have more than one meaning for example) that have a humorous effect, sounds mostly like a joke.
They say 'no pun intended' and it means that the person says something without the intention to make a humorous effect or a joke out of it.
Some examples of such play on words:
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" I used to be twins. My mother has a picture of me when I was two."
" What is the difference between a conductor and a teacher?
The conductor minds the train and a teacher trains the mind. "
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