[1] The discovery of motional narrowing has been attributed to Nicolaas Bloembergen during his thesis work in the 1940s[2] A common example is NMR.
As a consequence, when detecting the resonant rotation frequency, the linewidth is smaller (narrower) than it would be if the atoms were stationary.
The motional narrowing manifests in a peculiar temperature dependence of spin dephasing: The dephasing becomes slower at higher sample temperature where the exciton velocity becomes larger and the excitons more quickly experience environments with different magnetization.
However, if the nearby molecules reorient and move around fast enough, the vibration will essentially occur at an averaged frequency, and therefore have a smaller linewidth.
For example, simulations suggest that the OH stretch vibration linewidth in liquid water is 30% smaller than it would be without this motional narrowing effect.