The new Samsung Experience stores are very similar to the mini Stores that are already at several Best Buy locations. They'll be staffed by trained Samsung employees to help you learn how to use your Samsung phone or tablet or perform software updates.
The new Samsung stores are yet another page out of Apple's playbook. One of the biggest advantages to owning an over anything else is that you get free support for your device at any Apple Store. By plugging into 1,400 Best Buy locations, Samsung will be able to offer a similar advantage to its customers.