In short: in modern times a Royal Court is just the organization which keeps the monarchy running. In essence it is very the same as any ministerial department serving a minister (read: the King) which is lead by the Secretary-General (read: the Lord Chamberlain, the Court Marshall, the Grandmaster), which has a Secretary, often divided into a private and an official one, which has a financial controller (read: the Treasurer), etc.
In the novel A Dark Wood Wandering by Hella S. Haasse, the story focuses on Charles de Valois, Duc d'Orléans (1394-1465) the shy nephew of the mad king Charles VI of France. Here the situation is told in the 15th C. The Duke would marry three times, with Isabella de Valois, daughter of his nephew the King. Then with Bonne d'Armagnac and finally with Marie de Cleves. In the novel the a so-called Hofstaat (Dutch/German) which maybe is best translated as Court Estate, is often mentioned and described. It was very important and was even part of a dowry. The prestige of a lord or lady became visible in his or her Court Estate. A person like the Duchess d'Orléans had younger Duchesses, Marchionesses, Countesses etc. in her Court Estate, completed with a governor, a treasurer, a surgeon, a confessor, a comedian, artists, etc. In those times they were not part of a castle or palace (as the Court was always and ever on the move) but formed a part of the personal entourage. Not only the money, the jewels, the artworks, but also the exact Court Estate which was given to a lady was an important part of the negotations about a dowry.
This is still visible in the Swedish court organization. Where most monarchies have one court organization working for the whole Royal House, in Sweden some functionaries still belong to a Hofstaat, the Court Estate of a specific person. In Sweden there is the Konungens Hovstat med Kansli (the King's Court Estate with Chancellery), the Dronningens Hovstat (the Queen's Court Estate) and the Kronprinsessans Hovstat (the Crown Princess' Court Estate). In the Queen's Hovstat there are (female) advisers (Statsfru), secretaries, Hovdams (ladies-in-waiting). led by the Överhovmästarinna (Mastress of the Court). This organization model still shows how today's court organizations, much more efficient, leaner and meaner than ever before, were once the products of personal Court Estates which formed part of a person's entourage.