The three golden lions passant guardant on a red field were used in English royal coats of arms from Richard I on, and are part of the royal arms today.
The three gold fleur-de-lis on a blue field were adapted from the the French royal coat of arms, representing the Trinity. This simpler version of the French arms (previously, more fleur-de-lis were used) was included in English royal coats of arms from 1400 until 1603, based on the English claim to the French throne.
The quartering of the two was used by kings from Henry IV through Henry VIII including by Elizabeth of York's father and later by her husband. This four-part combination is shown twice: in the four elements making up the left half of the coat of arms, and again in the upper quadrant of the right half of the coat of arms.
The cross gules (red cross on a gold field) represents the de Burgh family; Elizabeth de Burgh had married Lionel of Antwerp, the second (surviving) son of Edward III.
An element with blue and gold stripes and a white shield at the far lower left. This represents the Mortimer arms.
