LILO is the Linux Loader. GRUB is the Grand Unified Boot Loader. Both do the same job. Each has advantages and disadvantages, but in a general sort of way LILO was most common in the past, but GRUB is most common now. Your best bet is to go with the default for your distribution unless you find a really good reason to go with the other one. Considering the question, I am guessing that you are fairly new to Linux, and probably don't have a specific reason for one or the other, so go with the default.