Why does the campfire not spawn at the player?

You're trying to set the campfire's position to a model. Model's don't have a position value, but the things inside of the model do. You should notice that this creates an error on the developer console (press F9 in-game when you try to spawn the campfire)

local player = game:GetService("Players").LocalPlayer
local character = game:GetService("Players").LocalPlayer.Character
local Campfire = game:GetService("ReplicatedStorage"):WaitForChild("Campfire")

script.Parent.MouseButton1Click:Connect(function()
    if player.Sticks.Value >= 2 and player.Stone.Value >= 1 then
            player.Stone.Value = player.Stone.Value -1
            player.Sticks.Value = player.Sticks.Value -2
            local ClonedCampfire = Campfire:Clone()
            ClonedCampfire.Parent = workspace
            ClonedCampfire:MoveTo(Character:WaitForChild("HumanoidRootPart").Position + (Character:WaitForChild("HumanoidRootPart").CFrame.lookVector * 3)) 
    end
end)

You may notice that I used :MoveTo(), this is a function that allows you to move every part of a model with one function. You can read more about it here

In order to make it spawn in front of the player, you'll want to use CFrame.lookVector.