Earlier this month, Twitter announced it is "testing a new way for you to discover and buy products on twitter".
The idea is that as you scroll through your twitter feed, you will see a tweet with a product and you will be able to purchase with just a few clicks. It looks as if the entire experience will occur on Twitter rather than passing you over to the merchant's website. This allows the user experience to be consistent from merchant to merchant and also allows Twitter to make it easier for you to purchase other products after your initial order.
It looks like Twitter will capture the information and then send the order to the merchant who will then process the transaction and fulfill the order.
This isn't the first time we have seen social commerce. Facebook had a Gifts program that allowed merchants to sell their products through their marketplace and Facebook users could send their friends gifts. This however was more of a marketplace idea where the user would browse to find a gift. Facebook gifting was shut down on August 12. Twitter's approach seems to be a more targeted offer to purchase that will probably align with their ad program.