Somehow, I stumbled onto this thread that is many years old, but given that it was answered incorrectly, I thought I would explain the term. The phrase is written as "a-whole-nother"; not "a whole nuther". This device is called a "tmesis" and is employed by taking a word - such as another - splitting the word in two and interjecting another word in between the two split parts. It is typically done to add emphasis. The most common example is taking "absolutely" and turning it into "abso-f***ing-lutely". As an example of how "a-whole-nother" is used: Let's say your boss asks you about a task. You want to tell your boss something like, "That's another issue!" to indicate that that issue has some sort of positive or (typically) negative aspect to it aside from what you're currently discussing. Using the tmesis device allows you to add that emphasis, "That's a-whole-nother issue!". HTH, Tom

It means a completely different story. "Nuther" is a slang form of "another". So the person is saying "that story is a whole different story" but splits "a-nother" and puts whole in between to make "a whole nuther story." It's very common to hear that in speaking. It's not standard writing, however. You might see it in chat, though.