a thing.py

from tkinter import *

class App:
    def __init__(self, master):

        frame = Frame(master)
        frame.pack()

        self.start = Button(frame, text = "Begin", command = self.start_up)
        self.start.pack()
        
        self.end = Button(frame, text = "End", command = frame.quit)
        self.end.pack()

    def start_up(self):
                
        temp = New_window()
   

class New_window: #Manages the new window

    def __init__(self):

        self.top = Toplevel() # top should be a member of New_window, so add self.
        self.top.title("Back and forth!")

        self.message = "Hit Previous or Next"
        #removed pack() from here, only need to pack() tk widgets like textboxes and buttons etc.

        # Create buttons
        # needs to be self.top and self.top.destroy
        self.quit = Button(self.top, text = "QUIT", command=self.top.destroy)
        self.quit.pack(side=LEFT)

        #needs to be self.top
        self.prev = Button(self.top, text = "Previous", command=self.prev)
        self.prev.pack(side=LEFT)

        #needs to be self.top
        self.nxt = Button(self.top, text = "Next", command=self.nxt)
        self.nxt.pack(side=LEFT)

        # Create text box
        # Renamed to textbox, and top changed to self.top
        self.textbox = Text(self.top, width = 20, height = 2, wrap = WORD)
        self.textbox.grid(row = 1, column = 1)
        self.textbox.pack() # have to pack() the textbox here

        self.mess_update() # added this to update the textbox with the initial
                           # "Hit Previous or Next" message 

    def nxt(self):
        self.message = "Moving forward" # changed to self.message
        self.mess_update() # added brackets, without them the function isn't called
        
    def prev(self):
        self.message = "Let's go back" # changed to self.message
        self.mess_update() # added brackets, without them the function isn't called
        
    def mess_update(self):
        # renamed to self.textbox
        self.textbox.delete(0.0, END) 
        self.textbox.insert(0.0, self.message) # changed to self.message


        
root = Tk()
app = App(root)
root.mainloop()