HOMO : The highest occupied molecular orbital
LOMO : Lowest unoccupied molecular orbital.
The term Band gap means the difference between energies of the HOMO and LUMO. It will also used for measuring the excitability of the molecule. If the energy is smaller than more easily the atom will get excited.
For example, to obtain the molecular orbital diagram, we need to know its place in periodic table. Then we will proceed from left to right.