method of initial rates
Imagine you want to learn how a car's acceleration depends on how hard you press the pedal. The cleanest test is to measure the speed right at the start, before traffic, hills, or a dropping fuel level muddy the picture. The method of initial rates does the same for a reaction: it watches the speed in the very first moments, before complications set in.
Concretely, it is an experimental technique for finding a reaction's order in each reactant. You run the reaction several times, each time changing the starting concentration of just one reactant while holding the others fixed, and you measure the rate right at the start (when essentially no product has formed and the reverse reaction is negligible). Comparing how the initial rate changes when you double a concentration tells you that reactant's order: no change means zero order, doubling means first order, quadrupling means second order.
The method matters because it is the standard, reliable way to pin down a rate law from data, and it sidesteps the messiness of products building up or reverse reactions kicking in. Its honest limitations: you must be able to measure the rate quickly and accurately at the outset, and it reveals the rate law only near the starting conditions, so behaviour later in the reaction must be checked separately if it might differ.
Run a reaction three times. Doubling [A] doubles the initial rate (so it is first order in A); doubling [B] quadruples the initial rate (so it is second order in B). From these comparisons alone you build the rate law rate = k[A][B]², and one more measurement gives k.
Change one concentration at a time and watch how the starting rate responds.
Vary only one reactant's concentration per trial; change two at once and you cannot tell which one caused the rate to shift. This 'one variable at a time' discipline is the heart of the method.