It is Chaenomeles japonica, popularly known as Japanese quince or Japonica. It is not the same as true quince, which grows on a tree that looks like a pear tree. But you can use it in the same way if you want to, though there is some disagreement over whether it is tasty or not - maybe it depends upon the variety, there are many varieties of C. japonica, or ripeness. The most popular suggestion seems to be including one chopped up in an apple pie, for example.