Domestic Medium Hair is a coat description, not a breed. It's the label used for mixed-ancestry cats whose fur falls between short and long, usually with a fuller tail, tufts between the toes and a soft undercoat, but without the heavy ruff of a true longhair. They come in every color and pattern, from tabby and tuxedo to calico and solid black.
Because their ancestry is mixed, size, personality and health vary from cat to cat. Most are medium-sized and sturdy, weighing roughly 6 to 14 pounds. Expect to brush a few times a week, more in spring and fall, and remember that the best guide to temperament is spending time with the cat.