It means that the person has used some words which produce some kind of word joke, but they didn't mean to make a joke. Usually a pun is a kind of play on words. So sometimes people mean to make a pun, but other times they say something and they don't mean to make a word joke, so they say so, to make it clear. For example the words son/sun are pronounced the same so we can make a joke using those. There are many other words in English which can be used to make a pun or word joke. For example if someone makes a pun I could answer "Very punny" which would be making a joke with the word "pun" that sounds like "fun". Instead of saying "funny" I say "punny".

The vast majority of times, "no pun intended" is used to draw attention to the pun that was just made. Since the preceding pun may not be readily apparent, it can help the reader go back a few words and catch the pun. Personally I don't use this phrase much, but I'm not a very punny person. More examples http://ask4essay.com/thread/what-does-no-pun-intended-mean/

A pun is a play on words, a joke exploiting meanings of words or words that sound the same. (Warning: Sometimes they're funny, other times they're terrible and boring XD) This is a pun: http://ak-hdl.buzzfed.com/static/enhanced/web05/2012/6/6/14/anigif_enhanced-buzz-2448-1339009167-14.gif The original saying is "I whip my hair back and forth." The word 'hare' sounds like 'hair.' That's the pun. So when someone says "no pun intended," they previously said something that could have been taken as a joke. They're saying that it wasn't meant to be a pun.