Fermi energy is often defined as the highest occupied energy level of a material at absolute zero temperature. In other words, all electrons in a body occupy energy states at or below that body's Fermi energy at 0K.
This concept of Fermi energy is useful for describing and comparing the behaviour of different semiconductors. For example: an n-type semiconductor will have a Fermi energy close to the conduction band, whereas a p-type semiconductor will have a Fermi energy close to the valence band.
Fermi energies of different material types. Source: http://commons.wikimedia.org/wiki/File:Band_filling_diagram.svg
As a material's temperature rises above absolute zero, the probability of electrons existing in an energy state greater than the Fermi energy increases, and there is no longer any constant highest occupied level, so while the material's Fermi energy may be useful as a reference, it is not very useful at real temperatures.
Instead, we can approximate the average energy level at which an electron is present is with the Fermi-Dirac distribution:
where E is the energy level, k is the Boltzmann constant, T is the (absolute) temperature, and E_F is the Fermi level. The Fermi level is defined as the chemical potential of electrons, as well as the (hypothetical) energy level where the probability of an electron being present is 50%.
Sources:
http://en.wikipedia.org/wiki/Fermi_level
http://en.wikipedia.org/wiki/Fermi_energy
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html
http://www.eng.umd.edu/~dilli/courses/enee313_spr09/files/supplement1_carrierconc.pdf
http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics
http://web.ift.uib.no/AMOS/PHYS208/larsP-N/p-n-slide-lars.pdf
http://courses.washington.edu/overney/FermiEnergy.pdf
http://faculty.kfupm.edu.sa/COE/elrabaa/rich%20text/coe360/Week2/Lec4%20SEP16.pdf