Say you're walking down the Target store's baby aisle. You've seen some brands (Gerber, Johnson & Johnson, and Carter's) at other stores, but only at Target can you find Up & Up. This Up & Up brand is the Target store's specialty brand.
This "white-labeling" is one way Target gets you as a customer to keep coming back to its store; Target is the only place you will be able to find this brand.
The term "white-label" comes from the white label on a package that has the marketer's branding and logo. When a company "white-labels," it simply means that another company will be rebranding one of its products or services to make it appear as the purchasing company's own.
White-labeling almost sounds like a negative, practically illegal action... but in reality, the white-label process is something agreed upon by both parties. The product or service is bought out by the company that then brands it as its own, providing business for the producing company and allowing the rebranding company to provide a service it wouldn't be able to do otherwise.
What You Can White-Label
Products are frequently white-labeled and sold in stores under a different brand name than the actual manufacturer, but surprisingly enough, services (even online ones) can be white-labeled, too.
For example, grocery stores often will offer a cheaper "store brand" version of a lot of cereals. This is a version of white-labeling in which other companies produce cereal, sell it to grocery stores, and allow the stores to put its own branding on the cereal.
Have you seen grocery stores and department stores that offer photo services like digital transfers, printing, and more? Many companies offer a white-label to those stores, so they don't have to do the work themselves on site.