Why does this animation script when i press a key not working?

It does not work due to the fact that KeyDown is deprecated. Instead, use ContextActionService. And as previous answers said, you defined the player as LocalPlayer but used player.

function playAnimation()
    local plr = game:GetService('Players').LocalPlayer
    local anim = script.Animation
    local track = plr.Character.Humanoid:LoadAnimation(anim)
    track:Play()
end

game:GetService('ContextActionService'):BindAction(
    "PlayAnim",
    playAnimation,
    false,
    Enum.KeyCode.One
)

This will work since it has no deprecated code.

It doesn't work cause you defined your player as LocalPlayer and later used player

What you can do to fix it is just to change every place where you have player in your script to LocalPlayer

Basically what they are both saying is that you forgot to put a space between local and player, lol.

It's because you declared your variable as LocalPlayer but are trying to reference it by typing player. In fact, Lua automatically will show a blue line under variables it considers undefined (The blue lines under player in your screenshot).

The fixed code would change LocalPlayer to player or player to LocalPlayer:

wait(2)

player = game.Players.LocalPlayer
local Mouse = player:GetMouse()
Anim = script.Animation

Mouse.Keydown:connect(function(key)
    if key == '1' then
        a = player.Character.Humanoid:LoadAnimation(Anim)
        a:Play()
    end
end)

Also, KeyDown is deprecated, meaning there is a better newer different version of it you should use instead. If you are comfortable with keydown thats fine, but it's better to use UserInputService or ContextActionService. Check out this page on the wiki:

http://wiki.roblox.com/index.php?title=Keyboard_input