It used to be (and for some cloth users still is) that a diaper service could come collect your dirty diapers, and return the clean. Nowadays, most people use disposable diapers, but diaper service is still available in a different way.
No more running to the store in the middle of the night for more diapers or making a make-shift diaper out of a dish towel! Modern mothers (and other caregivers) can have diapers delivered right to their front doors! It works like grocery delivery services. You sign up online, and once a month you receive a box of diapers in the mail. The only thing you have to do is change the size accordingly when baby outgrows the current one.
Amazon.com offers this service under their "Subscribe and Save" section. If you order a monthly shipment, then you pay less. What a great way to save time and money!