The structure of the Lua folder can be confusing. This page tries to layout where script files should go. If a folder is not mentioned here, you should not put your scripts into it unless you know what you are doing.

lua/ (Same as addons/<addonName>/lua/)

autorun/ - A folder for automatic scripts load and include on Lua start, both clientside and serverside.

client/ - Clientside only autorun scripts.

server/ - Serverside only scripts.

properties/ - A Folder for properties in The Context Menu.

bin/ - A folder for external binary modules. (Creating Binary Modules)

derma/ - A folder for derma utils.

drive/ - A folder for drive system classes.

effects/ - Scripts placed here will be automatically attempted to be loaded as Lua effects. (util.Effect)

entities/ - Scripts placed here will be automatically attempted to be loaded as SENTs. (Structures/ENT)

includes/ - A folder for Lua libraries and additional stuff used in other scripts. Runs first.

extensions/ - A folder for extended libraries. For example table library already exists but extensions/table.lua extends it.

modules/ - A folder for libraries.

matproxy/ - A folder matproxy stuff.

menu/ - A folder used for Menu state.

postprocess/ - Run by client on startup, typically contains Sandbox Post Processing effects.

skins/ - A folder for users derma skins.

vgui/ - Clientside folder for UI panels.

weapons/ - Scripts placed here will be automatically attempted to be loaded as weapons. (Structures/SWEP)

gmod_tool/stools/ - (Sandbox only) Scripts placed here will be automatically attempted to be loaded as tools. (Structures/TOOL)

gamemodes/

<gamemodename>/ - A folder containing gamemode files.

entities/ - Basically lua/ folder that is only loaded when the gamemode is. Subfolders are exactly the same as mentioned above.

gamemode/ - Folder contains all gamemode files. init.lua and cl_init.lua must exist in it.