How can I make the mouse recognize when I click a character's body part?

The Mouse object has a Property called Target. This resembles the object your curser is on.

Get the Mouse's Target in a Button1Down event - you can use an if statement to check if the Target's Parent has a Humanoid object, and decrease health.

(The mouse object can only be accessed from LocalScripts - put a LocalScript in any bin that replicates to the client; e.g. StarterPack, StarterGui, StarterPlayerScripts)

local plr = game.Players.LocalPlayer; --Player
local mouse = plr:GetMouse(); --Player's mouse

function LeftClick()
    local targ = mouse.Target; --This is what the mouse is on
    if targ then --If the mouse is actually on something
        --Search for a Humanoid
        local potentialHum = targ.Parent:FindFirstChild("Humanoid");
        if potentialHum then --If there's a Humanoid

            print("Damage da enemy >:3");

        end
    end
end

mouse.Button1Down:Connect(LeftClick) --Button1Down event on mouse

Click Select