Essentially, this is the plot:
When a system (such as a semiconductor) is in thermal equilibrium and no bias (voltage, EM radiation, ecc) is applied, the distribution function that describes the occupation of the quantum states is the Fermi-Dirac distribution (FDD), given by
f_0(E,E_F,T) = \frac{1}{e^{(E-E_F)/k_B T} +1}
where E is the energy of the state, EF is the Fermi energy (also called Fermi level), and T is the temperature. This distribution law is valid for any energy level of the system, independently of the fact that it is above or below the Fermi energy (conduction or valence band state).
When the system is under bias, the FDD doesn't hold anymore. However, if the bias is not to great, or not changing to quickly, it is still possible to describe the occupancy of the quantum states of the different bands using a distribution law of the same form of the FDD, but with different Fermi energy for different bands (One says that there is a situation of quasi-thermal equilibrium). Hence one has
f_c = f_0(E,E_{F_n},T)
f_v = f_0(E,E_{F_p},T)
where fc and fv is the probability of finding an electron in the conduction and valence band, respectively, and EFn and EFp are called the quasi Fermi levels for the conduction and the valence band.
You can look at the topic by this point of view:
Let us suppose that a semiconductor is in thermal equilibrium (no bias). Its density of free carriers in the conduction band (electrons) and in the valence band (holes) is given by
n = \int_{E_c}^{\infty} {g_c(E) f_0(E, E_F, T) dE}
p = \int_{-\infty}^{E_v} {g_v(E) ( 1 - f_0(E, E_F, T) ) dE}
where Ec is the CB minimum, Ev is the VB maximum and gc and gv are the density of state of the CB and VB, respectively. Suppose that a photon field now hits the systems. This rise both n and p and it is impossible to describe this new (quasi) equilibrium by means of the last two formulas, unless one replaces the single parameter EF with the two parameters EFn and EFp:
n_{bias} = \int_{E_c}^{\infty} {g_c(E) f_0(E, E_{F_n}, T) dE}
p_{bias} = \int_{-\infty}^{E_v} {g_v(E) ( 1 - f_0(E, E_{F_p}, T) ) dE}
Physically, the quasi Fermi level relative to a band is the effective Fermi level that brings to the same density of carriers in the same band when the system is not perturbed.
Since, in the example above, n_{bias} > n and p_{bias} > p (photons increase both carrier densities), one has E_{F_n} > E_F and E_{F_p} < E_F.
For more details you can read Chapter 3 of The Physics of Solar Cells by J. Nelson or many other books.
