For simplicity, take s orbitals.
when two s orbitals A and B overlap, you have two cases. Either their wave functions have same sign or they have opposite signs.
when they have opposite signs, the waves are out of phase, hence destructive interference takes place and hence there is no electron density at the part where they tried to overlap, that is between their nuclei. This is called anti-bonding.
$$\psi_u=N(\psi_A-\psi_B) $$