It's basically a two-part cup with an inner cylinder that you can freeze overnight. To use it, you freeze the cylinder, place it back in the cup, pour the drink/liquids of your choice into the cylinder, and stir with the provided spoon as the drink freezes.
They recommend using it with Starbucks Via instant coffee and milk but you can pretty much try it with whatever you like.
The Frozen Drink Maker is currently available for sale in stores and online in Japan for 3000 yen (~$27.22). If you don't live in Japan, you can probably find it on eBay.
It's a less kiddy, more expensive take on the anime-inspired ice cream makers that KFC Japan put out back in 2013 (which I find more entertaining plus would score me points with the nephews).
Photo via Starbucks Japan.