“autres” is meant to emphasize the difference between “nous” and the other people.

For my intuitive knowledge (and thus maybe wrong), this marks a clear difference between the subject group and the rest of the world.

“Nous autres, on sait faire la cuisine”: suggests that the non-cited implicit group does not know how to cook, for example.

The meaning is not the same as “nous”

• The “autres” form is rarely used in France French.
• I’ve never ever heard the “Eux autres” form however.

I’ve read a discussion on the grammar of this a while ago.

Basically nous-autres and vous-autres correspond to the emphatic forms “moi”, “toi” and “lui”, particularly in topic/comment construction (because “nous” and “vous” lack separate object forms): “nous-autres, on sait cuisiner”, “vous autres, je peux pas vous sentir” etc. The extension to eux-autres is a natural analogy. (English does not have this construction, which is close to cleaving)

I do not know what the specific etymology is (and @Oct’s seems like some awfully pop-whorfian approach to me), and the etymology of many grammatical constructions is not very well known anyway. There is a sociolinguistic element to it, since it’s not a formal construction, so it tends to be marked as low-class.

I went and looked at my Grevisse (14th ed.), with the caveat that it is an analysis of mostly written, European French (though it does often discuss regional usage). The relevant sections are §358 a), discussing adjectives applied to pronouns, and 659 h), on reinforced pronouns (autres discussed in the same context as -même). In both instances there is a brief mention of opposition/separation, but he also notes that there is a marked correlation with topic/comment-life construction, which in the Quebec dialect/sociolects we are discussing, will actually require the -autres forms.

I think a sensible argument is that what was originally an emphatic form (remember that this topicalization is already an emphasis!) was generalised to topicalizations as a whole (and a few others: “chez” can also sometimes be used with -autres pronouns without cleaving): a proper cleft sentence “C’est à nous-autres qu’ils l’ont donné” is also valid.

If you have taken a Spanish course, you know that “nosotros” is the first person plural pronoun. In Spain, similarly, “vosotros” is the familiar second person pronoun. This parallels the “nous-autres” construction. The construction is not common in France due to the promotion of the Parisian dialect as the standard, but I’m guessing it was far more common, particularly in the south, in the 18th century. You should see from what parts of France the common settlers of Quebec came, and when. There you will find part of the answer to “autres.” And before you ask, no, I don’t know this myself; I’m just speculating.

In Catalan, we = nosaltres and you pl. familiar = vosaltres.
In Gascon, we = nosautres and you pl. = vosautres. (Both reflect “we others” and “you others” as an additional distinction in person.)
I’m surmising that this Canadian (and Cajun) form reflects an older French that did not “evolve” along with Parisian French because of the geographic and cultural rupture.

In the southern part of Italy we hear noi-altri and voi-altri. It is not grammatical correct in Florentine Italian but in the dialects it is what people say. Spanish seems to be the only one of the romance languages that kept the “other” vosotros is vos-otros/otras and nosotros is nos-otros/otras.

Someone told me that this usage came about because the Christians wanted you know they were the believers and the other, Jews, Muslims et ali, were outsiders. I have no idea if that is true or not. However, I have never seen that form used in written Latin. They used nos and vos.

Please know, everything I just wrote is based on my knowledge of Latin which I teach, of Italian, my native language, of Spanish my almost native language, of French which I can read well but speaking is rough, and English which I used because I live in the States.

Valete, Arrivederci, Adios, Aurevoir, Good-bye