Unlike some more modern countries the purpose and function of the Royal Coat of Arms for the United Kingdom  is to identify the person who is the Head of State, in this case the Sovereign or Queen. And this design can be modified and changed with each Sovereign as they choose.

In the design of the Royal Coat of Arms the shield shows the royal emblems of the different parts of the United Kingdom: the three Tudor lions of England in the 1st and 4th quarters, the harp of Ireland in the 3rd quarter and the lion of Scotland in the second quarter.

Devices and Charges on the Royal Coat of Arms - Their history.

The Tudor Lions  - It's interesting that England is represented by the red Tudor lions passant on a gold field. The Tudor's (and their lions) are actually Welsh by descent from Rhodri Mawr, King of Wales in 841 from which the royal Tudors (or Twydr's) descend. After the Battle of Hastings,  the lions became accepted as the Royal symbols of English Tudor King. The original meaning of the King Rhodrick's lions was the triplication of his lion, indicating of  the division his lands and territories (whole of Wales) into three kingdoms for his three sons - north, south and Powys. The Welsh culture anciently has both mother and father passing on their properties evenly amongst their children being both matrilineal and patrilineal in tradition. This even handed approach on the Royal Coat of Arms with the double display of the Tudor lions, some say one for England and one for Wales marks the respect of the Royal Coat of Arms for all founding countries that make up the United Kingdom.

The Scottish Lion - The lion of Scotland descends from the days of William the Lion in the 1200's.Gervase of Canterbury described William as
'a man of outstanding sanctity ... much preferring to have peace than the sword and to provide for his people by wisdom rather than iron'.

The Irish Harp - This is one of the tantalizing hints of history of the Irish folk. Tradition has it that the harp of Ireland, shown on the arms, dates back to prehistory days of the Reign of the Tuatha de Dannan, the Dannan brothers and their famous Palace of Tara and apparently comes from a tale/tradition of a magical musical oracle who played the harp, warning of trouble, guiding the brothers and the Irish people through time. Modernly the harp conveys a combination of the good luck and history of the Irish people forward from about 1220 B.C.(or 1700 B.C. ibid Irish Pedigrees by John O'Hart.) 

The Royal Coat of Arms - Motto

 Surrounded by the motto of the Order of the Garter  " HONI SOIT QUI MAL Y PENSE" (Evil to him who thinks Evil) is testimony to a long history of the United Kingdom with the policies and politics surrounding the many civil and religious upheavals that weave through the history of Britain. The politics within the Catholic Church, the formation of the Protestant, the welcoming of the Jews, the expulsion of the Jews, then welcome again, the splintering of faiths and finger pointing all reflect the continuing change in  opinion and approach to peoples differences. 
     At time of writing, I believe that this particular motto dates back to King Henry VII who had a noted exasperation politically with the question of "Whom exactly ruled his country, a foreign faith leader or himself, the king? Another interesting tidbit about King Henry VII - ever hear the following nursery rhymes?
    "Oranges and Lemons ring the bells of St. Clements"
    "Ring around the Rosy"
    "Hickory, dickery dock the mouse ran up the clock"
    "As I was going to St. Ives, I met a man with seven wives"
     The above rhymes and more are actually attributed to Henry himself as the author who loved to amuse himself and friends by making up rhymes and songs that were mostly political satire at himself and his opponents at court. They of course were repeated from the court, to servants and staff to the countryside, although Henry wasn't the only political satirist of his day by far, just more prolific. There are fun sides of history. I say "attributed" as there are claimants to many songs of the day since - for in those days the "anonymous" was a great way to avoid what could be political suicide in those days, even for a king. Back to the Royal Coat of Arms

The Shield is supported by the English lion and the Scottish unicorn and surmounted by the Royal crown. The plant badges of the United
Kingdom - rose, thistle and shamrock - are often displayed beneath the shield. While we have discussed the English lion above, I am at a loss to see why the unicorn is Scottish. If you know - let me know please. The only Coat of Arms that I've been able to find in Scotland as yet is the Cunningham clan who use the unicorn's head as a device. So perhaps the meaning of the unicorn, aside from today's modern beliefs, trace back to the various orders of Knights, particularly the Knights Templar who were the Masters of the the Mystic and Magical in defense of christianity and the people of faith.

Below the Coat of Arms is the motto of the Sovereign
DIEU ET MON DROIT
(God and My Right)