It actuality is a shortened version of "another" - which is used by many people, even those who practice using grammatical correctness. It occurs naturally when the person is speaking too fast, and the sound of the letter "a" comes across as: an out going breath of air, or at a much lower octave than usual; therefore sounding absent. To write, "nother" rather than "another" is actual a "written vocalization" to emphasize haste, or pertinence, which otherwise, needs an entire phrase or sentence to drive the point home.
However, the colloquial frequency of the usage of "nother" slowly got carried into a variety of word groupings.
As the letter "a" is phonetically an out going breath at a certain octave, a rapid speech makes the "a" inaudible as anything except for the breath. (likewise the letter e is an incoming breath at a different octave).
It most frequently is found at the beginning of a sentence or directly after the word "And" as the second word of the sentence. By making the habit of trying to always say "and" before the word "another", it often corrects the problem in hurried speech. In relaxed or hurried speech, when there is failure to articulate the "d" sound in the word, then the phrase "And another" (when rushed) becomes "An nother" which still sounds like "another" to the listener. This does not always work, the outcome heard is often "an_another" or "ananother" when heard, which is worse than just saying "nother." It is quite possible that "another" is a word that was originally derived from the phrase "and other" as a transition in relaxed speech.
2)"Nother" a variation of "other." Often, in the more severe colloquial instances it is grouped in the middle of a sentence right after the word "no" in which case the "nother" is the equivalent of "other" Recently popular discussions about the very popular phrase "whole nother thing" fails to mention that this is a combination of relaxed annunciation and relaxed grammar. Where those who elect to write down the phrase put "whole nother thing" it is much more often pronounced: "whole nuddah thing" Which is just bad, all the way around. It is often used in personal story telling of a series events linked together, and adds flavor to the long winded conversationalists. It is more likely to be heard in an argument, when the whole emphasis is on not having one's own view point contested. It is effective, because it is obvious that when someone says "nuddah" they aren't concerned about being corrected or hearing your opinion. Where the "th" is replaced by dd (like a reversed Hispanic or Latin translation) It is found heavily used in areas that had a strong Euro-Spanish background, but are predominantly English speaking communities. For example "New Orleans, Louisiana."
"Nother thing ..."
"And nother thing is that.."
"Nother time I...."
"Nother way to go is..."
"whole nother time" (pronounced nuddah and is most effective when you stretch out the word "whole" and "time")
"I ain't gonna get no nother one of those, ever"
(It is a highly mindful statement to reinforce the sense of commitment to the decision. Most users of such language also know quite well how to speak properly and do so when required)