You would typically do this when you use a geometry manager (pack, place, or grid).

Using grid:

import tkinter as tk

root = tk.Tk()
for row, text in enumerate((
        "Hello", "short", "All the buttons are not the same size",
        "Options", "Test2", "ABC", "This button is so much larger")):
    button = tk.Button(root, text=text)
    button.grid(row=row, column=0, sticky="ew")

root.mainloop()

Using pack:

import tkinter as tk

root = tk.Tk()
for text in (
        "Hello", "short", "All the buttons are not the same size",
        "Options", "Test2", "ABC", "This button is so much larger"):
    button = tk.Button(root, text=text)
    button.pack(side="top", fill="x")

root.mainloop()

Configuring a button (or any widget) in Tkinter is done by calling a configure method "config"

To change the size of a button called button1 you simple call

button1.config( height = WHATEVER, width = WHATEVER2 )

If you know what size you want at initialization these options can be added to the constructor.

button1 = Button(self, text = "Send", command = self.response1, height = 100, width = 100) 

If you want these widgets to be really perfectly aligned with one another, it's definitely better to align them on the same grid and use the sticky argument to make the buttons stretch to fill their cell:

import tkinter as tk

root = tk.Tk()

chLabel = tk.Label(root, text="Channel group")
channelButtons = tk.Frame(root, bg='yellow')
ch1Button = tk.Button(channelButtons, text="CH1 Settings")
ch1Button.pack(fill='x')
ch2Button = tk.Button(channelButtons, text="CH2 Settings")
ch2Button.pack(fill='x')
ch3Button = tk.Button(channelButtons, text="CH3 Settings")
ch3Button.pack(fill='x')
ch4Button = tk.Button(channelButtons, text="CH4 Settings")
ch4Button.pack(fill='x')

trigLabel = tk.Label(root, text="Trigger group")
trigButton = tk.Button(root, text="Trigger Settings")

horizLabel = tk.Label(root, text="Horizontal group")
horizButton = tk.Button(root, text="Horizontal settings")

# Align the labels and buttons in a 2-by-3 grid
chLabel.grid(row=0, column=0, pady=10)
trigLabel.grid(row=0, column=1, pady=10)
horizLabel.grid(row=0, column=2, pady=10)
channelButtons.grid(row=1, column=0, sticky='news')
trigButton.grid(row=1, column=1, sticky='news')
horizButton.grid(row=1, column=2, sticky='news')

root.mainloop()

You would typically do this when you use a geometry manager (pack, place, or grid).

For example, you need to call pack on each of the buttons. See example of pack below.

    import tkinter as tk
    
    root = tk.Tk()
    for text in (
            "Hello", "short", "All the buttons are not the same size",
            "Options", "Test2", "ABC", "This button is so much larger"):
        button = tk.Button(root, text=text)
        button.pack(side="top", fill="x")
    
    root.mainloop()

When there is only text in your button, your width and height will be based on character length, not pixel length. So, your window is defined as 600 pixels by 600 pixels, but your button is defined 15 text characters by 15 text characters, which is much more than 15 pixels :)

I added a second button and put text in both of them, exactly 15 characters, to show you exactly what's happening. More information can be found on this Tkinter Button information page.

from tkinter import *
window = Tk ()
window.title(" ")
window.geometry('600x600')

btn = Button(window, text ="X"*15, bg = "white")
btn.config(height = 15, width = 15)
btn.grid(column = 0, row = 0)

btn2 = Button(window, text = "X\n"*14+"X", bg = "white")
btn2.config(height = 15, width = 15)
btn2.grid(column = 1, row = 0)

window.mainloop()

The width and height attributes are in units of characters (eg: 1 means the size of one average character). You can specify the width and height in units of pixels if the button has an image.

A button can have both an image and text, so a simple trick is to add a one-pixel transparent pixel as an image, which will then allow you to specify the size in pixels.

The padx and pady options also contributes to the size of the button. If you are trying to get a precise size, you need to set those to zero.

Here is a simple example:

import tkinter as tk

root = tk.Tk()
root.geometry("200x100")

pixel = tk.PhotoImage(width=1, height=1)
toolbar = tk.Frame(root)
toolbar.pack(side="top")
for size in (12, 16, 24, 32):
    button = tk.Button(toolbar, text=str(size), width=size, height=size,
                       image=pixel, compound="center", padx=0, pady=0)
    button.pack(side="left")

root.mainloop()

Regarding your initial question: the button does appear physically. The problem is, since it is so large, it is hard to distinguish from the rest of the window.

Now, you said that your ultimate goal is to change the size of a button. If so, then you are on the right track: you use the height and width options for this.

However, I would recommend that you make a few changes to your code:

1. Don't make the button so huge. Even on a very big monitor, having a button be that size is way overkill.
2. Don't make the window so huge. Nobody wants an application that takes up the entire screen.
3. Use .grid instead of .place. Doing so will make it easier for you to place widgets where you want them.
4. Set the height and width options when you make the button, not after it.
5. There is no need to import sys here. Only import what you need.
6. Don't import like this: from tkinter import *. Doing so dumps a whole bunch of names in the global namespace that can easily be overwritten.

Here is my version of your script:

import tkinter as tk

def mmWindow():
    mmWindow = tk.Tk()
    mmWindow.geometry('600x600')

mWindow = tk.Tk()
# You can set any size you want
mWindow.geometry('500x500+0+0')
mWindow.title('DMX512 Controller')

wtitle = tk.Label(mWindow, text="Pi DMX", fg='blue')
wtitle.grid(row=0, column=1)

# You can set any height and width you want
mmbutton = tk.Button(mWindow, height=5, width=20, text="Main Menu", command=mmWindow)
mmbutton.grid(row=1, column=1)

mWindow.mainloop()