Compare this, without using nonlocal:
x = 0
def outer():
x = 1
def inner():
x = 2
print("inner:", x)
inner()
print("outer:", x)
outer()
print("global:", x)
# inner: 2
# outer: 1
# global: 0
To this, using nonlocal, where inner()'s x is now also outer()'s x:
x = 0
def outer():
x = 1
def inner():
nonlocal x
x = 2
print("inner:", x)
inner()
print("outer:", x)
outer()
print("global:", x)
# inner: 2
# outer: 2
# global: 0
If we were to use global, it would bind x to the properly "global" value:
x = 0
def outer():
x = 1
def inner():
global x
x = 2
print("inner:", x)
inner()
print("outer:", x)
outer()
print("global:", x)
# inner: 2
# outer: 1
# global: 2