Scene.bin (256 files) - Contains all enemy data. AI, Text, enemy names, enemy move names, enemy HP and stats. Everything enemy related.
Kernel.bin - Contains programming data for many things related to menu and battle, like weapon attributes and strengths etc etc. Get Wallmarket and have a look. Also contains the lookup table for battle, so when you edit Scene.bin, this usually needs updating too.
Kernel2.bin - Contains only text for the menu. Names of materia, descriptions, names of items, names of enemy skills, names of limit breaks, Also contains "Ex-SOLDIER" name tag. Contains most of the battle strings like "Couldn't steal anything..."
Battle.lgp - Contains data for battle models. Not sure exactly what else.
Flevel.lgp - Contains all game dialogue (except world map). Contains game backgrounds and walkmesh. Contains turorial dialogue.
Please note, on PSX kernel2.bin does not exist because kernel.bin contains those files. When they ported to PC they made the text related parts of kernel.bin become kernel2.bin. Why? I dunno.