second-order kinetics

Suppose you double the amount of nucleophile in your flask and the reaction goes twice as fast; double the substrate too and now it's four times as fast. That doubling-of-doubling behavior is the signature of second-order kinetics, and it is exactly what an SN2 reaction shows. The reaction rate depends on the concentrations of two species, multiplied together.

Written out, the rate law is rate = k[R-X][Nu], first order in the substrate and first order in the nucleophile, so second order overall. The reason is mechanical: SN2 happens in a single step in which the substrate and the nucleophile must collide and react together. The slowest (and here the only) step — the rate-determining step — involves both molecules, so both appear in the rate law. The molecularity of that step is two (bimolecular), which is the "2" in SN2.

Kinetics is how chemists read a mechanism from the outside, without ever seeing a single molecule react. If the rate climbs when you add more nucleophile, the nucleophile must be in the rate-determining step — pointing to SN2. If the rate ignores the nucleophile entirely and depends only on the substrate, the nucleophile comes in after the slow step — pointing to SN1. Measuring how the rate responds to each concentration is one of the cleanest ways to tell the two pathways apart.