The Royal Coat-of-Arms is to be seen on many buildings, documents and even retail products (due to the by appointment to HRH schemes) in the United Kingdom.

A graphical description follows.
descriptions by me, questions answered at
The coat consists of a Royal Shield, adorned with the Crown and flanked by a Lion on the left and a Unicorn on the right (as viewed). Two mottos intertwine the whole.

Royal Shield
The shield bears the royal emblems of the different countries of the United Kingdom: the three lions of England in the first and fourth quarters (moving clockwise from top-left), the lion of Scotland in the second and the harp of Ireland in the third.

Garter surrounding the Shield
Bears the motto: "Honi soit qui mal y pense" (Evil to him who evil thinks)

Crown atop the shield
Is the standard Royal Crown graphic: topped by a Maltese cross, with beads flanking down to a sumptious red velvet interior, and the gold crown itself having crosses (N,W,S,E) and fleur de lis (NW, NE, etc) at the major compass points about it's circumference.

The Lion
Stands to the left, his tail fanning out like the head of a rose. He holds the shield, and his mane sweeps the garter. He wears the Royal Crown described above.

The Unicorn
Stands to the right, with a smaller crown around her neck, a heavy chain passes behind her back and she also holds the shield.

The Motto
Weaving across the bottom of the shield is the motto "Dieu et mon droit" (God and my right).

from the official Royal FAQ: "The function of the Royal Coat of Arms is to identify the person who is Head of State: in respect of the United Kingdom, the royal arms are borne only by the Sovereign. They are used in many ways in connection with the administration and government of the country, for instance on coins, in churches and on public buildings. They are familiar to most people as they appear on the products and goods of Royal Warrant holders."