Hovering over a part doesn't work, help?

When I tested your code I recieved the error: Players.TreacherousTale.Backpack.LocalScript:8: attempt to index field 'Target' (a nil value)

To fix this, you must check whether mouse.Target = true.

Furthermore, when the mouse hovers from Item1 to nil (the skybox), the infogui doesn't disappear. To fix this I checked whether mouse.Target = nil, and if it did then you'd set infogui.INFO1.Visible to false.

local UserInputService = game:GetService("UserInputService")
local mouse = game.Players.LocalPlayer:GetMouse()
local infogui = game.Players.LocalPlayer.PlayerGui:WaitForChild("InfoUI")

function hover()
    if mouse.Target then -- Check if there is actually a Target
        if mouse.Target.Parent.Name == "Item1" then 
            infogui.INFO1.Visible = true
            infogui.INFO1.Position = UDim2.new(0, mouse.X, 0, mouse.Y)
        else
            infogui.INFO1.Visible = false
        end

    else
        infogui.INFO1.Visible = false -- If there isn't a target, make the infoUI invisible

    end
end

mouse.Move:connect(hover)

You weren't exactly clear on what the problem was so I tried my best with what I was working with. I hope I helped!