Homo is Highest occupied molecular orbital and Lumo is Lowest occupied molecular orbital
Let’s understand this with example
Molecular Orbital electronic configuration for B2 σ1s2, σ*1s2 σ2s2, σ*2s2, π2px1= π2py1
Here in case of B2 highest occupied molecular orbitals are π2px and π2py and lowest unoccupied orbital will be σ2pz
Similarly in case of O2 HOMO are π*2px and π*2py and Lumo is σ*2pz
The gap between homo and Lumo decides Many properties of the molecule this gap can be treated as ionisation energy of the molecule.
When we provide energy (heat) to any molecule electrons from HOMO move to the excited State i.e. Lumo and when electron jump back to HOMO energy radiated in the form of light and this is reason behind the color of any molecule because molecule shows color corresponding to the wavelength light energy emitted during this transition
If gap between HOMO and LUMO is large compund can not show any color like in the case of O2 gap between HOMO & LUMO is very large but F2 & Cl2 shows color because gap is not so large.
If gap between HOMO & LUMO is large molecule will be more stable and gap is small molecule will be less stable