local GUIs when clicked on a player?

I would personally not use click detectors. They're deprecated, and there're much nicer methods :)

First of all, we should make a reference to the mouse:

local mouse = game.Players.LocalPlayer:GetMouse()

Then we set up a function that's fired whenever the player clicks:

mouse.Button1Down:connect(function()
	-- Clicked
end)

Then we can see what the player's mouse is currently hovering over by using the mouse.Target method, then we check if the mouse target is a body part of a player's character:

local target = mouse.Target
if target ~= nil and game.Players:FindFirstChild(target.Parent.Name) then
	-- Hovering over a player
end

(We also make sure target ~= nil to avoid any errors)

We can now get the player we're hovering over and for example display their name.

local player = target.Parent
print(player.Name)

All together thus far:

local mouse = game.Players.LocalPlayer:GetMouse()

mouse.Button1Down:connect(function()
	-- Clicked
	local target = mouse.Target
	if target ~= nil and game.Players:FindFirstChild(target.Parent.Name) then
		-- Hovering over a player
		local player = target.Parent -- (note that this is the player's character)
		print(player.Name.." was clicked on!")
	end
end)

Great, so now that we can print out the player's name that we're looking over we should start working on the Billboard GUI that you wanted. You'll start by designing the entire billboard gui as you want it to look (using placeholder names and values for their stats). Then you parent the gui to the StarterGui. We will now simply set the adornee of the gui to the player's body to display it over them!

Let's start by setting up a reference to the gui at the beginning of our script.

local gui = game.Players.LocalPlayer:WaitForChild("PlayerGui"):WaitForChild("BillboardGui")

Now all we need to do is set the adornee and the the names/values once you click on a player:

gui.Adornee = player.Head
gui.Frame.PlayerName.Text = player.Name
gui.Frame.PlayerKills.Text = game.Players:FindFirstChild(player.Name).leaderstats.Kills.Value

All in all it should look something like this:

local mouse = game.Players.LocalPlayer:GetMouse()
local gui = game.Players.LocalPlayer:WaitForChild("PlayerGui"):WaitForChild("BillboardGui")

mouse.Button1Down:connect(function()
	-- Clicked
	local target = mouse.Target
	if target ~= nil and game.Players:FindFirstChild(target.Parent.Name) then
		-- Hovering over a player
		local player = target.Parent -- (note that this is the player's character)
		print(player.Name.." was clicked on!")
		-- Setting up the gui!
		gui.Enabled = true
		gui.Adornee = player.Head
		gui.Frame.PlayerName.Text = player.Name
		gui.Frame.PlayerKills.Text = game.Players:FindFirstChild(player.Name).leaderstats.Kills.Value
	else
		-- Hide the gui if none is being inspected (target wasn't a player)
		gui.Adornee = nil
		gui.Enabled = false
	end
end)

For the sake of the example I just assumed that you used a leaderboard with the "Kills".