The HOMO-LUMO gap is also called the "band gap". It refers to the potential energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Basically, it's how much energy you have to feed into the molecule to kick it from the ground (most stable) state into an excited state.
For fullerenes, this may be related to their ability to generate photocurrent (like in a solar cell, light goes in and electricity comes out). A large band gap means you have to use high-energy light, like UV wavelengths. A small band gap means you don't need as much energy to excite the molecule, like green or even red wavelengths.
Aside from photocurrent, excitation can also drive other types of chemical reactions.