Why is this not doing a smooth movement in the Y axis ?

The camera jitters in the Y-axis whenever the player climbs a slope because the rate in which the Y changes is too slow (especially if the slope isn't steep). If the player jumps, you won't notice the jitter in the camera because the change in Y is big.

Instead of moving the camera at a fixed increment, try making it so that it goes part of the way (20%, for example) every frame.

I've also refactored and documented your script, which should take care of movement in all axes.

-- the offset of the camera in relation to the player. It is 10 studs to the left, 20 studs above, and 20 studs away from the player
local CamOffset = Vector3.new(10, 20, 20)
-- the direction in which the camera looks at. z = -1 means that it looks towards the player.
local CamLookDirection = Vector3.new(0, 0, -1)

local camera = game.Workspace.CurrentCamera
local player = game.Players.LocalPlayer
local RunService = game:GetService('RunService')

local function setupCamera()
	-- constructs the CFrame for the camera. You should probably check if HumanoidRootPart exists yet.
	camera.CoordinateFrame = CFrame.new(player.Character.HumanoidRootPart.Position + CamOffset, player.Character.HumanoidRootPart.Position + CamOffset + CamLookDirection)
end
player.CharacterAdded:connect(setupCamera)

local function onUpdate()
	if player.Character and player.Character:FindFirstChild('HumanoidRootPart') then
		-- lerps (linearly interpolates) the camera every frame. Each frame, it is 20% closer to its destination(0.2 == 20%).
		camera.CoordinateFrame = camera.CoordinateFrame:lerp( CFrame.new(player.Character.HumanoidRootPart.Position + CamOffset, player.Character.HumanoidRootPart.Position + CamOffset + CamLookDirection), 0.2 )
	end
end
RunService:BindToRenderStep('Camera', Enum.RenderPriority.Camera.Value, onUpdate)