I am trying to make a toggle invisibility, how would I do so?

I suggest creating a folder inside of ServerStorage to store the player's Accessories.

Also that 'grey block' that is around the player's torso is the HumanoidRootPart. It's default transparency is set to 1, and when you're getting all the parts inside the Character you're also getting the HumanoidRootPart and setting the transparency to 0.

local ss = game:GetService("ServerStorage")
local Event = game.ReplicatedStorage.InvisEvent
local isInvis = false

Event.OnServerEvent:Connect(function(Player)
	
	local Character = Player.Character
	
	if isInvis == true then
		isInvis = false
		
		for _, part in pairs(Character:GetDescendants()) do

			if part:IsA("BasePart") or part:IsA("MeshPart") then
				part.Transparency = 1

			elseif part:IsA("Accessory") or part:IsA("FaceInstance") then

				if not ss.PlayerAccessories:FindFirstChild(Player.Name) then
					local PlayerAccessoryFolder = Instance.new("Folder")
					PlayerAccessoryFolder.Name = Player.Name
					PlayerAccessoryFolder.Parent = ss.PlayerAccessories
				end
				part.Parent = ss.PlayerAccessories[Player.Name]
			end
		end	
	else
		isInvis = true
		
		if ss.PlayerAccessories:FindFirstChild(Player.Name) then
			
			for _, Accessory in pairs(ss.PlayerAccessories[Player.Name]:GetChildren()) do
				if not Accessory:IsA("FaceInstance") then
					Accessory.Parent = Character
				else
					Accessory.Parent = Character.Head
				end
			end
			
			for _, part in pairs(Character:GetDescendants()) do
				if part:IsA("BasePart") or part:IsA("MeshPart") then
					if part.Name ~= "HumanoidRootPart" then
						part.Transparency = 0
					end
				end
			end
		end
	end
end)

Hope this helps.

If you have any questions just post a comment to this answer and I'll try to answer them.