What is the difference between a LocalScript and a Script in Roblox?
To expand on Robert Harvey's answer, Scripts (also known as "Server Scripts" or "Normal Scripts") run on roblox's servers, and can make changes to the game that affects all players. LocalScripts (also known as "Client Scripts") run directly on the player's computer itself, and for the most part, can only make changes to the game that affect the player whos computer the scripts are running on. However there is an exception: If the server sets the "Network Ownership" of a part to a certain player, then that player's LocalScripts can move that part around, and all other players will see that change. This is automatically done with all player's Characters to eliminate apparent latency when controlling your own character.
It should also be noted that to communicate between LocalScripts and Scripts one must use "Remote Events" or "Remote Functions".