Catafalque comes from the Italian word catafalco, which means scaffolding. It is the term used for a bier or platform that supports a coffin, and catafalques are often, although not always, moveable. In the image here, Napoleon’s body rests on the catafalque in the lower left of the image. The slant-sided base or table which supports his body is the catafalque.
In the United States, the most iconic example of a catafalque is the Lincoln Catafalque, which was created for Lincoln’s funeral in 1865. This pine platform covered with black cloth remains in the Exhibition Hall at the U.S. Capitol’s visitor center, but has been called into service regularly (with new cloth and some additional supports) since 1865 for all those who have lain in state in the Capitol Rotunda. Lincoln’s funeral train traveled back to Springfield, Illinois, stopping at a number of cities along the way, so many catafalques were no doubt built for the ceremonies held in those cities, but the one in Washington is the one created for his funeral service there.