The Berliner Rathaus (Berlin town hall), designed by Hermann Friedrich Waesemann and completed in 1869, houses the government of the federal state of Berlin, led by the mayor of Berlin (currently the Social Democrat Klaus Wowereit). Its colloquial name, Rotes Rathaus (red town hall), refers to the colour of the bricks it's built from, rather than being anything to do with its politics, though it did serve as the town hall of communist East Berlin.
The area between it and the Marienkirche (St Mary's church) was cleared of buildings after World War II, a pedestrianised square with trees, fountains and flowerbeds taking its place. The perfect place for a Christmas market!
The wooden huts are a feature of virtually every German Christmas market and help keep at least some of the cold winter weather off the stallholders inside.
In front of the Marienkirche (I'll save its history for another post) is the Neptunbrunnen (Neptune fountain) which once stood in front of the Berliner Stadtschloß. It was put into storage after the Schloß was demolished and put here by the Marienkirche in 1969. What Neptune, Roman god of the sea, would think of the fountain having a skating rink put around it is anyone's guess, but the Berliners seem to like it: