elementary step
Imagine describing a journey across a city. You could say 'I went from home to work' (the overall trip), or you could list each unbroken leg: walk to the station, ride the train, walk to the office. An elementary step is one of those unbroken legs of a reaction, a single event that happens in one continuous motion without any intermediate species appearing partway through.
In an elementary step, a small number of bonds break and form together in one concerted motion, passing over a single energy barrier (one transition state). Because it is a single physical event, its rate law follows directly from how many molecules must collide: if one molecule rearranges by itself the step is unimolecular and first order; if two molecules must meet it is bimolecular and second order. This is the one place in chemistry where you can read the rate law straight off the equation, which you absolutely cannot do for an overall reaction.
Mechanisms are built by stringing elementary steps together. The species that appear at the end of one step and are consumed by the next are the reactive intermediates. Understanding steps individually lets chemists pinpoint which one is slowest (the rate-determining step) and therefore controls how fast the whole reaction goes. A balanced overall equation tells you nothing about the steps; you must propose them and test them.
The acid-catalyzed reaction of an alkene often goes in two elementary steps: first the alkene grabs a proton to form a carbocation (slow), then the carbocation captures a nucleophile (fast).
Two simple legs make up the whole trip; each is one elementary step with its own barrier.
You can read a rate law directly from an elementary step's molecularity, but you must never do this for an overall (multi-step) equation, where the rate is governed by the slowest step and any steps before it.