It is a cast taken of a dead person's face.
This mask is of the Emperor Napoleon Bonaparte. He died on 5th May 1821 while in exile (banishment) on the Isle of St. Helena in the south Atlantic. The cause of his death is not known.
First, a mould is made by covering the face with a thin layer of plaster of Paris (the eyebrows and lashes are usually smeared with oil first to stop them sticking to the plaster). Once the first layer has begun to dry a second, thicker layer of plaster is added. When the outer layer has dried the whole mould is removed from the face.
Then the hollow mould is used to make the mask itself. Plaster, wax and metal are often used. The example below on the left is plaster. The example on the right is made from bronze.


It is generally thought that the best time to make a death mask is right after death.
The bronze version above on the right is a copy of an original mask. There are several different versions of Napoleon's death mask in circulation - after his death many people, including hero-worshippers, wanted to own a copy. A book has even been written on the subject (Les Masques Mortuaires de Napoleon by E. de Veaux).
This version is signed by one of the doctors present at Napoleon's bedside, Francesco Antommarchi. It is a version of a model he issued in 1833 and was produced sometime between 1839 and 1847.
There are a few different versions of the story as to how the mask was created. One version says that Dr. Antommarchi tried to take a cast and failed. Later Napoleon's English doctor, Francis Burton, successfully took a cast.
However, Madame Bertrand, Napoleon's attendant, managed to steal part of the cast, leaving Burton with just the ears and back of the head. He took Bertrand to court in an attempt to get the cast back but failed.
A year later Madame Bertrand gave Antommarchi a copy of the mask, from which he had several copies made. One of these he sent to Lord Burghersh, the British envoy (representative) in Florence, asking him to pass it to the famous sculptor, Antonio Canova. Unfortunately Canova died before he had time to use the mask and instead the piece remained with Burghersh. The National Museums Liverpool version, cast by E. Quesnel, is thought to be a descendent of that mask.