One thing __init__.py allows is converting a module to a package without breaking the API or creating extraneous nested namespaces or private modules*. This helps when I want to extend a namespace.
If I have a file util.py containing
def foo():
...
then users will access foo with
from util import foo
If I then want to add utility functions for database interaction, and I want them to have their own namespace under util, I'll need a new directory**, and to keep API compatibility (so that from util import foo still works), I'll call it util/. I could move util.py into util/ like so,
util/
__init__.py
util.py
db.py
and in util/__init__.py do
from util import *
but this is redundant. Instead of having a util/util.py file, we can just put the util.py contents in __init__.py and the user can now
from util import foo
from util.db import check_schema
I think this nicely highlights how a util package's __init__.py acts in a similar way to a util module
* this is hinted at in the other answers, but I want to highlight it here
** short of employing import gymnastics. Note it won't work to create a new package with the same name as the file, see this