In quantum mechanics the particles are indistinguishable, the uncertainty principle prevents knowing the path that each particle follows. Therefore, the wave function of a system of identical particles will not distinguish one particle from another. Let them be a set of particles, whose coordinates are $q_1,q_2,.....q_n$. The wave function will depend on the coordinates of all the particles that make up the system $\psi(q_1,q_2,.....q_n)$. This wave function can present two different behaviors when faced with the exchange of any two particles:
$\psi(q_2,q_1,.....q_n)=\psi(q_1,q_2,.....q_n)$, the function is said to be trade-symmetric. $\psi(q_2,q_1,.....q_n)=-\psi(q_1,q_2,.....q_n)$, the function is said to be antisymmetric with respect to swapping.
Pauli's principle , the wave function of a system of electrons (fermions) must be antisymmetric with respect to the exchange of any two electrons and must not distinguish between electrons.
In the case of bosons (particles with integer spin), the wave function is symmetric.