The first is pretty mundane in a way. Rather than the previous ad hoc arrangements, a Royal will now be assigned a Coat of Arms on his or he eighteenth birthday, marking their coming of age.
Secondly, the two Princes started a tradition of not just inheriting Coats of Arms from their father but also adding elements of their Mother's arms as well. This, in their case, was the Escallop (scallop shell or Shell of St James) from the Spencer Coat of Arms from Diana, Princess of Wales.
Traditionally, the eldest son of The Prince of Wales has carried a Label of three Points (an exception to the five points of any other grandchild of a Sovereign), the central one charged with the red Cross of St George. For instance, a previous eldest son of the Prince of Wales was HRH Prince Albert Victor, Duke of Clarence who was assigned such a label. With Prince William this central St George's Cross was replaced by a red Escallop (see above), a fitting gesture to the memory of his Mother and the start of a new tradition.
Prince Harry was, at the age of 18, assigned a Label of five Points with the centre and two outer points charged with the same red Escallop as his elder brother (see below). It was announced that, in time, as and when Prince Harry moves up a generation and becomes the son of a Sovereign, the two empty inner Points will be dropped and he will be assigned a Label of three Points all charged with the red Escallop.
As you will see from further entries this new tradition has been taken up by the children of the Duke of York and replaces the previous traditional charges of Anchors, Lions, Hearts and Roses, etc. Having said that, Prince Edward, the Earl of Wessex was assigned a Tudor Rose, so it will be interesting to see what Lady Louise Mountbatten-Windsor is assigned. And will Prince George and the baby who is on the way be assigned, say, acorns from their Mother's Coat of Arms? We shall see...