The floor you see today is covered in Victorian quarry tiles, dating from around the 1840's and possibly locally made. There were brickworks nearby, which gave a plentiful supply of terracotta, while the nearby River Trent provided good transport links.
Back in the 15th century, you would have stepped down into the Great Hall and found the floor flattened down and covered in 'Thresh' - short lengths of chopped straw, glued down with animal blood and compacted down by human feet. To stop thresh from drifting out of the door openings, a wooden strip was attached below the door - a "Thresh hold".
A good way to impress visitors in medieval times was by the installation of a tiled central fire area or a tiled walkway in front of the raised Dais; which supported the Top or High Table.
Terracotta literally means "Earth clay" –it's generally red due to the iron content, but can be other colours too. In the past, bricks and tiles were often fired in a "clamp". This is made by layers of clay objects and straw being built up into a stack. A large fire was lit on top and allowed to burn down through the stack, gradually heating up the clay to around 800 degrees, and sometimes higher temperatures were achieved.
Terracotta goes darker the higher the temperature it is fired to, so you tell how hot medieval kilns were depending on the shade. A very light orange indicates 800 to 1000 degrees. Deep red is closer to 1100. Higher temperatures were difficult to achieve and not particularly desirable. The terracotta becomes very dark and brittle as the iron content bloats and melts, the tiles would also be more prone to distorting which of course is no good for laying a flat floor.
Medieval tiles were not like the big utilitarian Victorian slabs, they would be small, maybe 3 or 4 inch square and inlaid with lighter coloured clays in heraldic patterns and designs, and crucially, they were often glazed.
Glaze was a thin layer of ground lead and sometimes flint applied to the surface of the tile and fired in a kiln. They can't be fired in a clamp- it would damage the shiny finish of the glaze, it requires a much more labour intensive wood fired kiln. This would be tunnel shaped, usually built on a slope to draw in oxygen, which generated temperatures of 1000 degrees or more, melting the lead to a smooth shiny finish. Lead glaze was (and still is) manufactured by heating and melting Galena, a mineral that can be found in abundance in the Peak District and other parts of the Midlands. Skimming off the top of the molten Galena you acquire a material called Litharge- a type of lead. Litharge was invariably contaminated with iron from the surrounding earth which results in the white clays used to inlay the patterns appearing yellow after firing.
None of this lengthy process comes cheap. At the end of the day the objective is to impress your visitors by demonstrating both your taste and your wealth!