Queen Elizabeth I's coat of arms

The Royal Arms have changed and evolved over the nine centuries since they were first used by Richard I (The Lionheart). Richard I's Coat of Arms was simply the three lions, referred to as 'Gules three lions passant guardant or'.  This remained the Royal Arms of England until King Edward III quartered the arms with the fleur-de-lis, the arms of the french kings, to symbolise his claim to the French throne. This remained the Royal Arms until the reign of James I, and thus are shown above in the Royal Arms of Elizabeth I. Elizabeth was officially titled Queen of France, but the title was a hollow one. Calais, England's last French territory, was lost in the reign of Mary I. James I quartered the arms further, adding the Scottish arms and the harp of Ireland. The Royal Arms was altered again by subsequent monarchs, but the simplified version adopted by Queen Victoria, remains the official Royal Arms today.

The Supporters to the arms (lions, unicorns, dragons etc) have also changed considerably over the centuries. Queen Elizabeth chose as her supporters the English Royal Lion (on the left) and the Welsh Dragon (on the right), symbolising she was Queen of England and Wales.

The crown is the obvious symbol of monarchy.

The motto on the coat of arms above "Semper Eadem" is the latin for "always the same" and was the personal motto of Elizabeth I. Sometimes the Queen's Royal Arms are depicted with the more standard royal motto "Dieu et mon Droi" (God and my right).
 

Related Sites:
The Royal Arms of Great Britain
Elizabethan Heraldry
Tudor Heraldry