Step 1: Recall what "rate independent of concentration" means mathematically.
For a reaction $A \rightarrow \text{Products}$, if the rate law is \[ \text{Rate} = k[A]^0 = k \] then the rate simply equals the rate constant no matter what $[A]$ is, since anything raised to the power zero is one. This is called a zero order reaction.
Step 2: Understand why such reactions behave this way.
This typically shows up in reactions happening on a fixed surface, such as a solid catalyst, or driven by a fixed intensity of light, where the amount of reactant present in the bulk no longer matters once the surface or the available photons become the limiting factor.
Step 3: Give a concrete example.
The decomposition of ammonia on a hot platinum surface is a textbook case: \[ 2NH_3(g) \xrightarrow{Pt,\ \Delta} N_2(g) + 3H_2(g) \] At high pressure, the platinum surface becomes completely saturated with adsorbed ammonia molecules, so adding more ammonia gas cannot speed the reaction up any further, the rate stays fixed at whatever the surface can process.
Step 4: State the final answer.
\[ \boxed{\text{Zero order reaction; e.g. decomposition of } NH_3 \text{ on Pt}} \]