Tkinter example code for multiple windows, why won't buttons load correctly?

I rewrote your code in a more organized, better-practiced way:

import tkinter as tk

class Demo1:
    def __init__(self, master):
        self.master = master
        self.frame = tk.Frame(self.master)
        self.button1 = tk.Button(self.frame, text = 'New Window', width = 25, command = self.new_window)
        self.button1.pack()
        self.frame.pack()

    def new_window(self):
        self.newWindow = tk.Toplevel(self.master)
        self.app = Demo2(self.newWindow)

class Demo2:
    def __init__(self, master):
        self.master = master
        self.frame = tk.Frame(self.master)
        self.quitButton = tk.Button(self.frame, text = 'Quit', width = 25, command = self.close_windows)
        self.quitButton.pack()
        self.frame.pack()

    def close_windows(self):
        self.master.destroy()

def main(): 
    root = tk.Tk()
    app = Demo1(root)
    root.mainloop()

if __name__ == '__main__':
    main()

Result:

You need to specify the master for the second button. Otherwise it will get packed onto the first window. This is needed not only for Button, but also for other widgets and non-gui objects such as StringVar.

Quick fix: add the frame new as the first argument to your Button in Demo2.

Possibly better: Currently you have Demo2 inheriting from tk.Frame but I think this makes more sense if you change Demo2 to be something like this,

class Demo2(tk.Toplevel):     
    def __init__(self):
        tk.Toplevel.__init__(self)
        self.title("Demo 2")
        self.button = tk.Button(self, text="Button 2", # specified self as master
                                width=25, command=self.close_window)
        self.button.pack()

    def close_window(self):
        self.destroy()

Just as a suggestion, you should only import tkinter once. Pick one of your first two import statements.

#!/usr/bin/env python
import Tkinter as tk

from Tkinter import *

class windowclass():

        def __init__(self,master):
                self.master = master
                self.frame = tk.Frame(master)
                self.lbl = Label(master , text = "Label")
                self.lbl.pack()
                self.btn = Button(master , text = "Button" , command = self.command )
                self.btn.pack()
                self.frame.pack()

        def command(self):
                print 'Button is pressed!'

                self.newWindow = tk.Toplevel(self.master)
                self.app = windowclass1(self.newWindow)

class windowclass1():

        def __init__(self , master):
                self.master = master
                self.frame = tk.Frame(master)
                master.title("a")
                self.quitButton = tk.Button(self.frame, text = 'Quit', width = 25 , command = self.close_window)
                self.quitButton.pack()
                self.frame.pack()


        def close_window(self):
                self.master.destroy()


root = Tk()

root.title("window")

root.geometry("350x50")

cls = windowclass(root)

root.mainloop()