A zero-order process is a process that has a constant rate. The rate a the zero-order process is the zero-order rate constant and it does not depend on the amount of the reactant involved in the process.

For example, when the drug elimination follows zero-order kinetics, the amount of the drug eliminated per unit time is constant and is equal to the zero-order rate constant.

In this case, the zero-order rate constant has units, of amount/time.