If we consider a number of identical, indistinguishable particles, then clearly interchanging a pair of particles is quite unobservable. This has two possible solutions These two cases have important physical consequences.
Particles obeying the two conditions have completely different behaviours.
Bosons have wave functions which are symmetric under the interchange of identical particles. Fermions have wave functions which are antisymmetric under the interchange of identical particles. They obey Fermi-Dirac statistics, showing destructive interference of identical single particle wave functions. In particular, no two identical fermions can occupy wave functions with identical quantum numbers. They include the constituents particles of matter.