Someone who's stony shows little emotion or sympathy for other people. As your math teacher hands back last week's geometry quiz, her stony face won't seem like a very good sign.
A face with a stony expression is so lacking in feeling that it is "like stone." The other way to use the adjective stony is to mean "with lots of stones," like when you talk about a stony blueberry field in Maine or a stony path leading up to a lush garden. Stony comes from the Old English stanig, with its root of stan, "rock or gem."