1. For more specific information, LUA is: http://rathena.org/wiki/Lua
for a simplified one, take a look at their file name (without _f). they explains the client (almost) every thing needed for your client to work. especially, with sprites.
One of LUA files usage is: custom items. (well, custom headgear or official (normal) headgears). First, server will tell the client that the ViewID for an item (let's say Goggles) is **** (I forget) (they're set on item_db). then, upon double clicking the Goggle item (upon wearing it), client will read datainfo/accessoryid.lua to translate the ViewID from item_db.txt to something like "[ACCESSORY_GOGGLES]", then it will open datainfo/accname.lua to get the real sprite name (something.act, something.spr). Then, you should be able to see your goggles on your head.
Another usage (for 2013 clients) is item description, item resource name. While previously we used idnum2itemdesctable.txt and so on, 2013 clients use lua files to replace them. therefore, this lua file will hold the description and the sprite name and item name to be shown for a particular item (System/iteminfo.lua lub) (2013 clients++)
2. If you have downloaded translated lua files, the files inside data/lua files/ are lub files. they're the compiled (encrypted) version of their source files (data/luafiles514/lua files).
it depends on how did you diff the client, to read lua files first or to read lub files first.