That Place is a void like dimension used by Goku and Vegeta during their training under Whis.
Overview
Goku and Vegeta being transported to That Place by Whis' Staff
During Whis' training, Beerus suggested that Whis send them to "That Place" so they could get stronger much faster. Using his Angel Attendant's Staff, Whis sent Goku and Vegeta into another dimension. Goku compared the space to the Hyperbolic Time Chamber though it differs in that it is a groundless void and contains an overwhelming atmosphere of Godly ki that prevented Goku and Vegeta from moving at first until Vegeta realizes they shouldn't let their ki leak out of their bodies. Goku concludes the dimension likely has a time differential like the Hyperbolic Time Chamber thus they need to find food and decide to head in the direction of Whis' staff which is the only thing within the void besides Goku and Vegeta. Vegeta and Goku manage to find some pizza Whis had stored within his staff. During their time there, Vegeta and Goku master Godly ki to the point they can use it to become Super Saiyan Blue. Their training, however, was interrupted when Whis summoned them back to retrieve his staff so he could retrieve one of the pizzas for Beerus only to discover Goku and Vegeta had eaten them all or they would have died causing an angry Beerus to chase them into the forest, while Whis discovered Bulma's message leading them to learn of Frieza's resurrection and invasion of Earth.
Video Game Appearance
That Place appears as a story exclusive stage during the Infinite History Saga in Xenoverse 2 as part of the Extra Pack 2 DLC, where it is named Inside Whis's Staff.