The Palace was originally built as the city hall of Amsterdam. It was then one of the worlds's miracles.
Since 1813 it is in use by the Royal House. They don't live there (nobody lives in the palace), but the Palace is used for official state visits, get-togethers of ambassadors etc. Before 1813 (during the French occupation), King Louis (brother of Napoleon) used the Palace as his residence.
When a new King or Queen is installed, the balcony of this Palace is the location for the welcoming balcony scene.
It is famous for its paintings, sculptures and furniture. It is generally open to the public, if not used for official occasions.
Balcony scene of the new King Willem-Alexander on April 30 2013, with his wife and 3 daughters.
Royal Palace Amsterdam