As Dr. Hugh Macartney pointed out in one of his articles, there were very few Arms issued to McCartneys. There is a commercial version of a McCartney Coat of Arms (shown below) which is available at any establishment that sells thing Irish. This device is not legitimate. It is a combination of a variety of Arms developed solely as a souvenir to be sold to unsuspecting tourists. This "tourist" version will be used as a means to explain some of the heraldic concepts.
In the terms of heraldry, this Coat would be described as "or a stag gules passant a bordure gules crested cubit arm palewise a rose gules". In English this would be translated as follows:
or - a gold or yellow field
a stag gules - the symbolic animal in red
passant - with right fore-leg raised as in walking
a bordure gules - surrounded by a red border
crested - having a crest above the shield
cubit arm palewise - a forearm and hand in a verticle position
a rose gules - a red rose
The final description would read as "a red stag walking on a gold field with a red border, under a raised arm holding a red rose".
Many families added mottos to their Arms. In this commercial version we see a latin motto "stimulat sed ornat". Thanks to Regis High School in New York City, my son, Michael, had a well rounded education which included Latin studies. He has translated the motto as follows:
stimulat, verb (stimulare): to goad, prick, vex; also, to annoy, incite, stir up (we get the English stimulate from this) - I'm quite sure it's 3rd person singular, making it "he stirs up".
sed, preposition: but, however; also used to confirm, as in "and indeed" or "and what's more".
ornat, verb (ornare): to equip, furnish, fit out; also, to adorn, decorate, embellish; to honor, distinguish (we get the English ornate from this) - this, too, is 3rd person singular, making it "he equips" or "he furnishes".
So, this makes the motto (loosely): "He stirs up trouble, and what's more he supplies the means to carry it out!". Or more simply and accurately (but less colorfully): "He incites, and indeed, he equips".
In the Oxford Guide to Heraldry the authors, Thomas Woodcock (Somerset Herald) and John Martin Robinson (Maltravers Herald Extraordinary), make reference to one of the earliest catalogings of heraldic symbols written in 1394, Tractatus de Armis by Johannes de Bado Aureo. de Bado Aureo stated the heraldic meaning of the stag as "poverty in youth and wisdom in war".
In Celtic legend, which pre-dates heraldry, the stag is a very powerful symbol. In early history, the stag in Ireland and Scotland was a very large and powerful animal. One of the rituals relating to leadership was to have the candidate hunt and kill a stag using only a knife made from a stag's horn. The person would then take on the persona of the stag, gaining its strength and wisdom.
Woodcock, Thomas, and John Martin Robinson; The Oxford Guide to Heraldry; Oxford University Press; 1988