Your shanks are your shins, the lower part of your leg. It hurts like crazy to bang your shank on the edge of a coffee table.
Shank comes from a Germanic source related to Schenkel, or "thigh." It's most common to talk about shanks in terms of meat, like lamb shanks or beef shanks, rather than your own shins. The shape of lower leg bones influence other ways shank is used, to refer to objects from drill bits to the narrow piece of a shoe's sole that connects to its heel. For unclear reasons, to shank means to hit a golf or tennis ball badly.