Sigma bonding is most simply defined for diatomic molecules using the language and tools of symmetry groups.
[2] Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix or hybridize.
As a practical consequence of this mixing of diatomic molecules, the wavefunctions s+s and pz+pz molecular orbitals become blended.
The extent of this mixing (or hybridization or blending) depends on the relative energies of the MOs of like symmetry.
The corresponding antibonding, or σ* orbital, is defined by the presence of one nodal plane between the two bonded atoms.
When viewed down the bond axis, a σ MO has a circular symmetry, hence resembling a similarly sounding "s" atomic orbital.