What does pun mean as in no pun intended?

Answer 1

A pun is a phrase or word that makes humour by relying on the different meanings of a word or words with similar sounds. A pun is often referred to as the lowest form of humour, and unlike jokes is often greeted with groans not laughter.

Examples of puns would be:

• Did you hear about the optometrist who fell into a lens grinder and made a spectacle of himself?
• There were two ocean tankers that collided. One was hauling red paint, one had blue paint. . At last report, the captains were marooned.
• Two peanuts walk into a bar. One was a salted.

No pun intended implies that a factual statement could be interpreted as a joke or pun, but that was not the intent:

Detective one: Looks like he was drowned in this vat of refrigerated blood at the slaughterhouse!

Detective two: Really? He was killed in cold blood? No pun intended!

Answer 2

A pun is a play on words. Sometimes, it is intended, where people make a silly joke about something and the words are cleverly (or not so cleverly) used to make use of their double meanings. For example- one person might say at dinner that the chilli con carne OS quite cold, then some joker might pipe up and say "yes, this chilli is quite chilly" at which point everyone else groans at the obvious and intended pun. Sometimes people are have a more serious conversation about something and a pun is said by accident- at which point they will say "no pun intended".