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Wash each quince in cool water. Stem and core the fruit and cut each one into chunks. Leave the peel intact. Place the pieces in a large soup pot or stew pot. Add enough water to cover all of the pieces by about an inch. Bring the water to a boil, reduce to a simmer, and cook the quinces for 45 minutes or so, until the pieces are soft.  To test whether the quince pieces are done, poke them with a fork. If the fork slides in easily, the quince is ready. Overcooking the quince will affect the flavor, so make sure it is simmering, not boiling, as it cooks. Use a potato masher to mash the quince into pulp, leaving no large lumps. The mashed quince should be slightly runny, like loose applesauce. Add a little water if it seems too thick. Set out a large bowl. Place a mesh strainer over it, and cover the strainer with a large piece of cheesecloth. Pour the quince pulp into the cloth-covered strainer. The juice will begin to run into to the bowl, while the pulp stays in the cloth. Let the pulp strain for about 4 hours.  Check the juice in the bowl every so often. You should end up with 4 to 5 cups after a 3 to 4 hours; if it doesn't seem as though you're getting enough juice, mix some water into the pulp and continue letting it drain. Use the back of a wooden spoon or a spatula to press the pulp when the straining time is nearing an end, to extract the last drops of juice.
Prepare the quince for cooking. Cook the quince . Mash the quince. Strain the quince.