A sarcophagus (plural: sarcophagi) is the stone container used to house a body when burial occurs above ground.
Another word is tomb.
The first people to make sarcophagi were the Ancient Egyptians, who used them as the outer container for a royal burial. Inside the sarcophagus there would be several more wooden coffins, so a sarcophagus is usually much larger than the person it contains.
Some sarcophagi were carved out of a soft pale yellow rock called alabaster. Others were carved from much harder granite. The outer surface was carved with an image of the dead person, together with many hieroglyphs representing good luck charms and references to the Book of the Dead and afterlife. They were all painted, although the paint has disappeared over the ages.
The Romans copied the Egyptian styles until they became Christians. After this, most Romans were buried.
In Christian times sarcophagi continued to be made for important people, and you will find them in many European churches and cathedrals. In Medieval times, the image of the person was carved on the top in a very elaborate way. The video shows a Medieval knight. The crossed legs indicate that he had been on a crusade. We would normally call these more recent stone boxes 'tombs'. These tombs were placed inside the cathedrals and churches, but that soon led to a shortage of space, and so it is rare to find a sarcophagus younger than Medieval times.
In the 18th and 19th centuries, people were buried and a false sarcophagus (usually called a tomb) placed over the burial site in the graveyard. So the stone tombs you see in churchyards today never contained a body. That is buried in the ground below. In this case the sarcophagus is simply to tell other people that the dead person was important or wealthy enough to be able to afford a grand memorial.