Application is step one. They see if you're qualified based on credit, criminal history, and income.
Step two is approval. They call you or contact you to let you know you were approved, and what the next steps are.
Step three is lease signing. You sign the lease, and get the keys. Before doing this, go through the place again, make sure it's cleaned and fixed up to your liking, photograph and document any deficiencies, and provide a list of said deficiencies to the landlord/management company. You may be fine with some deficiencies (provided they're cosmetic only), but documenting them ensures you won't be charged for them when you move out.