You could set up a callback to react to <Motion> events:

import Tkinter as tk
root = tk.Tk()

def motion(event):
    x, y = event.x, event.y
    print('{}, {}'.format(x, y))

root.bind('<Motion>', motion)
root.mainloop()

I'm not sure what kind of variable you want. Above, I set local variables x and y to the mouse coordinates.

If you make motion a class method, then you could set instance attributes self.x and self.y to the mouse coordinates, which could then be accessible from other class methods.

Here's a snippet to get the x,y position after a Button-1 click event:

from Tkinter import *

def getxy(event):    
    print("Position = ({0},{1})".format(event.x, event.y))

root = Tk()
frame = Frame(root, width=512, height=512)
frame.bind('<Button-1>', getxy)
frame.pack()
root.mainloop()

More on Tkinter events and bindings: http://www.pythonware.com/library/tkinter/introduction/events-and-bindings.htm

This will only update the Label when the mouse is inside the tkinter window:

No need to use win32api, tkinter has it built in. We can bind a function to root's <Motion> key and use the given positional argument event to retrieve the coordinates of the mouse.

from tkinter import Tk, Label

root = Tk()
label = Label(root)
label.pack()
root.bind("<Motion>", lambda event: label.configure(text=f"{event.x}, {event.y}"))
root.mainloop()

If what I said in my previous comment is what you're trying to do, since tkinter doesn't pause the program to wait for a mouse click event you will have to do this: it rebinds it every time the mouse button get clicked

from tkinter import *
from tkinter.filedialog import askopenfilename
from PIL import Image, ImageTk
import tkinter.simpledialog

root = Tk()

#setting up a tkinter canvas
w = Canvas(root, width=1000, height=1000)
w.pack()

#adding the image
File = askopenfilename(parent=root, initialdir="./",title='Select an image')
original = Image.open(File)
original = original.resize((1000,1000)) #resize image
img = ImageTk.PhotoImage(original)
w.create_image(0, 0, image=img, anchor="nw")

#ask for pressure and temperature extent
xmt = tkinter.simpledialog.askfloat("Temperature", "degrees in x-axis")
ymp = tkinter.simpledialog.askfloat("Pressure", "bars in y-axis")

#ask for real PT values at origin
xc = tkinter.simpledialog.askfloat("Temperature", "Temperature at origin")
yc = tkinter.simpledialog.askfloat("Pressure", "Pressure at origin")

#instruction on 3 point selection to define grid
tkinter.messagebox.showinfo("Instructions", "Click: \n" 
                                            "1) Origin \n"
                                            "2) Temperature end \n"
                                            "3) Pressure end")

# From here on I have no idea how to get it to work...

# Determine the origin by clicking
def getorigin(eventorigin):
    global x0,y0
    x0 = eventorigin.x
    y0 = eventorigin.y
    print(x0,y0)
    w.bind("<Button 1>",getextentx)
#mouseclick event
w.bind("<Button 1>",getorigin)

# Determine the extent of the figure in the x direction (Temperature)
def getextentx(eventextentx):
    global xe
    xe = eventextentx.x
    print(xe)
    w.bind("<Button 1>",getextenty)

# Determine the extent of the figure in the y direction (Pressure)
def getextenty(eventextenty):
    global ye
    ye = eventextenty.y
    print(ye)
    tkinter.messagebox.showinfo("Grid", "Grid is set. You can start picking coordinates.")
    w.bind("<Button 1>",printcoords)

#Coordinate transformation into Pressure-Temperature space
def printcoords(event):
    xmpx = xe-x0
    xm = xmt/xmpx
    ympx = ye-y0
    ym = -ymp/ympx

    #coordinate transformation
    newx = (event.x-x0)*(xm)+xc
    newy = (event.y-y0)*(ym)+yc

    #outputting x and y coords to console
    print (newx,newy)

root.mainloop()

Generally speaking you should never need to "get" this information because it is given to you as part of the event object that is passed in. You probably only need this information when responding to an event, and the event gives you this information.

Put more succinctly, to get the information you simply have to retrieve it from the event object.

Here's an example:

import Tkinter

class App:
    def __init__(self, root):
        f = Tkinter.Frame(width=100, height=100, background="bisque")
        f.pack(padx=100, pady=100)
        f.bind("<1>", self.OnMouseDown)

    def OnMouseDown(self, event):
        print "frame coordinates: %s/%s" % (event.x, event.y)
        print "root coordinates: %s/%s" % (event.x_root, event.y_root)

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