The Michaelis constant $K_m$ is numerically equal to the substrate concentration at which the reaction velocity equals half its maximum: $v = V_{max}/2$. It is a measure of enzyme-substrate affinity — a low $K_m$ indicates high affinity (enzyme is half-saturated at low [S]); high $K_m$ indicates low affinity. $K_m = (k_{-1} + k_{cat})/k_1$ where $k_1$ is association, $k_{-1}$ is dissociation, and $k_{cat}$ is the catalytic rate constant.