The concept of HOMOs and LUMOs important for a number of reasons.
First, in many organic reactions, the HOMO (highest occupied molecular orbital) of one molecule interacts with the LUMO of another molecule to form a new bond between them. In order for this to occur the orbitals must overlap when they come together. Understanding the shape of the LUMOs and HOMOs involved can tell you a lot about how a reaction works and what the products will be - or it might explain why a reaction does not work at all.
Second, the difference in energy between the HOMO and LUMO in a given molecule is (usually) the amount of energy it takes to get the molecule into an excited state. You can also use it to predict the colors of compounds and a number of other uses.