Kate first wore these earrings on the Royal Tour of Canada this year. She wore them again on her first solo overseas trip to The Netherlands.
These earrings are not unfamiliar to some of us. Anna of My Small Obsessions notes that both Queen Elizabeth II and Sophie, Countess of Wessex have worn them. Anna believes this pair belongs to the Queen and she loans them to other Royal women.
Update: The Telegraph has stated these were loaned to Kate by the Queen.
They are quite simple: a diamond stud on the earlobe and an egg shaped pear drop attached as a dangle. I have seen video of Kate wearing these earrings. The pearl moves freely so I can confirm that they are not stationary.
Here they are on Kate: