When should a local script or server script be used?

A LocalScript is a Lua source container that runs Lua code on a client connected to a Roblox server. They are used to access client-only objects, such as the player's Camera. For code run through LocalScripts, the LocalPlayer property of the Players service will return the player whose client is running the script. Source

A Script in Roblox is a type of object that holds a section of Lua code. A script will execute on the server and has access only to server-side events and properties. Source

LocalScripts should be used when something only effects 1 player, if it effects more than 1 person, or everyone needs to be able to see it you use a server script