So your customer finds something he loves in your store that he can't wait to buy. He clicks 'buy now' and proceeds towards the checkout. At the checkout page you can give your customer an option that allows him to inform you of when he'd like to have the product delivered. All he has to do is click the drop down menu of the 'when should the product be delivered option' and he can enter a date of his choice.
Learn how you can set this feature up in your store in this video.