Step 1: Km is the Michaelis constant from Michaelis-Menten enzyme kinetics, described by the equation \(v = \dfrac{V_{max}[S]}{K_m + [S]}\).
Step 2: By definition, Km is the substrate concentration at which the reaction velocity is half of the maximum, that is when \(v = V_{max}/2\). Substituting this into the equation gives \(K_m = [S]\) at that point.
Step 3: Km is therefore an indicator of enzyme affinity: a low Km means high affinity for the substrate, and a high Km means low affinity. The other options describe "twice", "thrice" or "one third" of Vmax, which have no kinetic definition and are simply incorrect.
Step 4: Hence Km is the substrate concentration at half-maximal velocity, Vmax/2, option (a).