Can someone clarify why some scripts only work in Edit mode?

I'm curious as to why some scripts only work in edit mode, and not when you publish it. I've had this problem before, and was given a solution, but I still don't understand why it does this. I've heard that it has something to do with the 'client' and the 'server' and stuff like that, but I don't truly understand what I keep doing wrong. Some justification is appreciated.

local player = game.Players.LocalPlayer
local Mouse = player:GetMouse()
local Char = player.Character
local Humanoid = Char:WaitForChild("Humanoid")



local animations = {1877306614,1877291193,01895620990}

local function Punch(plr)
local animation = Instance.new("Animation")
local picked = math.random(1, #animations)
animation.AnimationId = "http://roblox.com/asset/?id="..animations[picked]
local animTrack = Humanoid:LoadAnimation(animation)
animTrack:Play()
local dmgScript = script.DmgScript:Clone()
if picked == 1 then
    dmgScript.Parent = Char.RightHand
elseif picked == 2 then
    dmgScript.Parent = Char.LeftHand
elseif picked == 3 then
    dmgScript.Parent = Char.LeftFoot and Char.LeftLowerLeg
end
dmgScript.Disabled = false
wait(0.4)
dmgScript:Destroy()
end

Mouse.Button1Down:connect(function()
print("yup it worked")
Punch()
end)

This is inside a localscript inside of startergui ^^^

script.Parent.Touched:Connect(function(hit)
local char = hit.Parent
local hum = char:FindFirstChild("Humanoid")
if hum and char.Name ~= script.Parent.Parent.Name then
    hum.Health = hum.Health - script.Dmg.Value
    script.Disabled = true
    wait(0.5)
    script.Disabled = false
end
end)

This is inside a script inside of the script above ^^^

There is also an Int value inside of the normal script. ^^^