Text in Gui won't change?

Problem

You're getting the StarterGui, these changes will not show until you reset and respawn. StarterGui is not the PlayerGui.

Solution

You need to access the PlayerGui. PlayerGui will be located in the actual player. Once you change something in the PlayerGui, then you will see the changes. The variable number will also only be one since you keep replacing whatever the value is to 0 each time someone hits the brick.

Final Script

function onTouched(hit)
    local PlayerWhoHit = game.Players:GetPlayerFromCharacter(hit.Parent) --Set up a variable to find if someone hit the brick.
    if PlayerWhoHit then --PlayerWhoHit will either have a value or have nil. If it has nil, then the if then statement will be skipped.
        local gui = PlayerWhoHit.PlayerGui.PointsGui.PointsFrame.Points
        --local number = 0 --The number would be 1 each time you hit the brick, you can not have this variable inside the function. I also assume you're trying to up the number of the single player, so we just need to take the number from their gui and put it in here.
        local number = tonumber(gui.Text)
        if number == nil then number = 0 end --This is just in case the text of Points text is anything but a number.
        number = number + 1 --This line really isn't necessary, you can just do gui.Text = number + 1 on the next line, but I'll keep it around.
        gui.Text = number
    end
end

script.Parent.Touched:connect(onTouched)

Hopefully this answered your question, if it did do not forget to hit the accept answer button. If you have any questions, feel free to comment below and I will get back to you.

Your script is trying to access the StarterGui on this line :-

local gui = game.StarterGui.PointsGui.PointsFrame.Points

You need to access the players GUI e.g (this is from the wiki):-

-- Accessing PlayerGui from a Server Script:
game.Players.PlayerName.PlayerGui

-- Accessing PlayerGui from a LocalScript:
game.Players.LocalPlayer.PlayerGui

Edit:-

local gui = game.StarterGui.PointsGui.PointsFrame.Points -- replace this as show above as you need to reference the players gui

function onTouched(hit)
    if hit.Parent:FindFirstChild("Humanoid") then

    -- The second problem is here
        local number = 0 -- you create a new variable number and set it as 0
        number = number + 1 -- then you add 1
        gui.Text = number -- then you set this as 1 meaning that it will not change from 1

    end
end

script.Parent.Touched:connect(onTouched)

This is one way you could solve it (change the variable scope):-

local gui = game.StarterGui.PointsGui.PointsFrame.Points -- replace this as show above as you need to reference the players gui

 local number = 0 -- the variable is now outside so it will not be created inside the function, this means it will exist after the function finishes allowing you to add 1 to it. 

function onTouched(hit)
    if hit.Parent:FindFirstChild("Humanoid") then

        number = number + 1 -- then you add 1
        gui.Text = number -- then you set this as 1 meaning that it will not change from 1

    end
end

script.Parent.Touched:connect(onTouched)

This is just one way you could do it and this should only be used as an example as I do not know your game plan/design.