The Casa Rosada, also known as the Pink House, is the official workplace of the President of Argentina. The president doesn't live here. Their residence is in the northern suburb of Olivos (you can see the official helicopter bring them to/from the office each day if you pay attention!).
Why is it pink? There are a couple different urban legends. One is that President Sarmiento painted it with a mixture of white paint and cow's lard (tinged pink from the blood) to help protect the building from humidity.
Another possibility is that pink represented the unity between the two political factions. Red of the Federalists and white from the unitarians.