What does this mean in English: "Vulpem pilum mutare, non mores"?

Literally the translation should be: the fox loses his HAIR but not his habits.
Pilus = (a)hair. Compare French poil.
Skin = pellis.
Mutare is related to English moult.
French equivalent is: Le renard change de POIL, mais pas de moeurs ou de caractère.
English puts it differently:
The leopard cannot change its spots.

The wolf changes the skin not its habits.
Source: Vespasianus

I always thought the word for wolf in latin was lupum.

Literally you are right ,peasypod, and your answer more accurate.Congratulations!

Do foxes CHANGE their hair ( hair style, hair colouring, ..toupee) or do they LOSE it by molting ? They certainly do not change their SKIN.
The quote is from Suetonius Vesp. 16. "proclamaverit vulpem pilum mutare, non mores".
In Apost. 12.66 there is a Greek variant : o lukos tèn tricha ov tèn gnomèn. Here again tricha does not mean SKIN, but HAIR.
Various European languages use the equivalent of "to lose" to render this Latin saying.
German has Der Fuchs VERLIERT das Haar, und bleibt wie er war.
Dutch has: De vos verliest zijn haren, maar niet zijn streken.
The fact is that the fox LOSES its winterhair in spring, and CHANGES its summerhair at the end of winter.
It may be useful not to look at Latin as if its meaning could only be rendered in one language.
The meaning of mutare is of course "to change", but the meaning of "mutare pilum" need not be rendered in two words. It is perfectly possible to render it by "molting" or "moulting" as can be seen in the Online Etymology Dictionary where the Old English mutian is described as deriving from mutare and developing into "to molt" or "to moult". See http:// www.etymonline.com. Check for to molt.
To change hair is in my opinion more general in meaning than to molt. Molting is what happens in spring. Changing hair is probably the correct term for what happens in late winter.
No idea what Suetonius had in mind. It certainly is incorrect to translate PILUM by skin. Mutare pilum does not mean to "shed one's skin". Snakes shed their skin, not foxes. As is illustrated by online dictionaries such as http://www.thefreedictionary.com/pilus or encyclopedias such as https://en.wikipedia.org/wiki/Pilus and also any
good traditional Latin-English dictionary.

Italian which is close enough to Latin I would think has a proverb "Il lupo perde il pelo ma non il vizio." There is an alternative wording of this proverb: " Il lupo cambia il pelo, ma non i vizi".
Italian pelo (from Latin pilus) can be translated either as hair or as fur. Italian pelle (from Latin pellis) is "the skin".
A proverb is of course not the same thing as a translation of a quotation. If the Italians prefer to think of wolves, that's their good right. But it does not mean that Suetonius wrote vulpes and thought of a wolf.

Among the many different renderings of this quotation from Suetonius I found this Italian
one: La volpe cambia il pelo, non le abitudini.
You could render this in many ways.
What matters is that "il pelo" is either hair or "skin-with-hair" i.e. fur).
There is not such a thing as "the one and only correct translation".
Moreover the question was not: how should this be translated, but: what does it mean?
There is no doubt that a "vulpes" is not a wolf.
But it's obvious that in some languages people refer to the wolf's changing its summer- or winterskin rather than to the fox's.
Changing winterskin in actual fact comes down to "molting".
Changing summerskin comes down to growing extra fur.
A correct understanding of a Latin quotation requires more than finding an English equivalent for it. I guess that "The fox changes its skin but not its habits" is indeed "a" correct translation because "skin" here seems to "imply"
"the hair on the skin". But strictly speaking Suetonius uses the Latin word for hair, and not for skin. Pilum, sed non pellem.