After the delivery of the head, there's restitution, where the head externally rotates so that the shoulders can pass through the pelvic outlet and under the symphysis pubis.
And finally there's expulsion, where the anterior shoulder slips under the symphysis pubis, followed by the posterior shoulder, and then finally followed by the rest of the body.
There’s a muscle, called the puborectalis muscle, that loops around your digestive tract between those two sections, and it helps keep poop inside you when you aren’t trying to eliminate it.