elementary reaction
Think of a long journey broken into single steps you can take in one motion — one stride, one turn, one door opened. You cannot break a single stride into smaller strides; it is already the simplest unit of the walk. An elementary reaction is the chemical version of one such single stride: a reaction that happens in exactly one molecular event, with nothing simpler happening in between.
More precisely, an elementary reaction is a single step in a mechanism in which the molecules shown actually come together (or a single molecule falls apart) in one go, passing directly over one energy barrier from reactants to products. Because it is a real single event, its rate law can be written straight from the equation: the rate depends on the concentration of each reacting species raised to its number in that step. This is the one situation where you may read the rate law off the stoichiometry — something you can never do for an overall reaction.
Why it matters: every multi-step mechanism is built out of elementary reactions, so they are the true Lego bricks of kinetics. The honest caveat is that you cannot tell by looking whether a written reaction is genuinely elementary; calling a step elementary is a claim about reality that must be justified, and most equations you meet in a textbook are overall reactions, not elementary ones.
In a single elementary step, one ozone molecule (O3) bumps into one oxygen atom (O) and they combine into two O2 molecules. Because this is one true collision event, its rate is simply proportional to [O3] times [O] — read straight off the equation.
For an elementary step — and only then — the exponents in the rate law match the coefficients.
Molecularity (how many molecules take part in the step) is a property only of elementary reactions; order is a property of any rate law, measured experimentally. The two coincide just for elementary steps.