Why is the if statement I made not working?

You are checking the contents of the TextBox whenever the script is first loaded. What you are intending to do is check the contents of the TextBox whenever the GuiButton is Activated.

I have not over analyzed or made any additional changes to your code aside from this: Inside the loop, I am declaring a function for each GuiButton found which will be called when that GuiButton is Activated. Inside that function I am checking the contents of the TextBox using your method and then running the appropriate code.

local gui = script.Parent
local frame = gui.JournalFrame
local player = game.Players.LocalPlayer
local sound = script.Parent.JournalFrame.X.JournalCloseSound
local items = frame:GetChildren()
local Nouns = {"apple", "tree"}
local RemoteEvent = game.ReplicatedStorage.JournalEvent
local sound1 = frame.Success
local sound2 = frame.Book
local sound3 = frame.Error

for i, item in pairs(items) do
    if item:IsA("GuiButton") then
        item.Activated:Connect(function()
            if frame.Write.Text == Nouns[1] then
                local itemName = item.Name
                game.ReplicatedStorage.JournalEvent:FireServer(itemName, game.Players.LocalPlayer:GetMouse().hit.Position)
                player.PlayerGui.JournalGui.JournalFrame.Visible = false
                player.PlayerGui.MiniJournalGui.MiniJournalFrame.Visible = true
                player.PlayerGui.MiniJournalGui2.MiniJournalFrame2.Visible = false
                player.PlayerGui.JournalGui.JournalBackFrame.Visible = false
                player.PlayerGui.JournalGui.FailMessage.Visible = false
                sound:Play()
                wait(1)
                game.Players.LocalPlayer:GetMouse().Button1Down:Connect(function()
                end)
            else
                gui.FailMessage.Visible = true
                sound3:Play()
                wait(4)
                gui.FailMessage.Visible = false
                local itemName = item.Name
            end
        end) 
    end
end