Magento: How to enable backorders?

Difference between backorder and pre-order

A backorder is for an item that was in stock previously but is temporarily out of stock.
A pre-order is for an item that has not been released yet.

Scenario for backorder:

For example, a customer orders 3 items. One item is not in stock. Shouldn’t I be able to Invoice only the 2 items I am shipping now, and then go back in next week and Invoice for the third item when it is back in stock? How do I set this up? – Source: magentocommerce forum

Backorders simply means that the item you are going to order is out of stock and you will receive the item OR the item will be delivered to you when the item will be in stock.
By default, backorder is not enabled in magento. Hence, you cannot add items to cart when the item is out of stock. But, if you enable backorders then you can add item to cart even if it is out of stock.
To enable backorders, go to:
Admin Panel -> System -> Configuration -> Catalog Tab -> Inventory -> Product Stock Options -> Backorders = Allow Qty Below 0 and Notify Customer
Edit Product to Qty = 0 and Stock Availability = In Stock
And backorders are enabled!
When you add the particular product to cart, the product is added to cart and you will see the following message:
* This product is not available in the requested quantity. 1 of the items will be backordered.
You can order the product even if it is out of stock. The product will be delivered to you when it is in stock.