Irreducible representations and system states connection Let's say I have the molecule $\ce{N2+}$. Its symmetry point group is clearly $D_{\infty\mathrm h}$. But I'm confused by its irreducible representations. I know there are 8 of them, but as I understand it, they're all representations of the same group, just with different bases. 

But today I found out, that they're not completely "equal", i.e. that they mark different states of the system ($\mathrm{A_g}$ is the ground state, $\mathrm{B_{1u}}$ is one of the excited states etc.).

What I'm completely missing is - how are irreducible representations linked with the system states?

Please, try some "low-level" explanation, I'm a beginner both in quantum chemistry and group theory.
The symmetry of a state is the MO (molecular orbital) product of its occupied molecular orbitals. Let's take the example of water molecule. We can see the symmetry label of each of the MO in the diagram. Each MO is assigned an irreducible symmetry label (associated with the point group of molecule) which can be deduced from the symmetry of MOs in space (or from the LCAOs). The wavefunction associated with the MOs also have the same symmetry species. Now, this arrangement of electrons represents the ground electronic state of water, so the symmetry label of the ground state of water can be obtained as 

$(2a_1)^2(1b_2)^2(3a_1)^2(1b_1)^2=(A_1)^2\bigotimes (B_2)^2\bigotimes (A_1)^2\bigotimes (B_1)^2 =A_1$ 

Follow the same procedure to obtain ground state of $N_2^+$. Let me know if you have any questions.