Domestic Medium Hair is a coat description, not a breed. It covers mixed-ancestry house cats with fur between short and long: fuller than a shorthair, usually with a plumed tail, tufts between the toes and a soft undercoat, but without a heavy ruff. They come in every color and pattern, and most adults weigh 6 to 14 pounds.
Because the ancestry is mixed, personality, size and health follow each cat rather than a breed standard, so meeting the cat tells you more than the label does. The practical points are brushing, which matters most in spring and fall when the undercoat sheds, and indoor living, which keeps a cat safer from traffic, wildlife and disease.