The Hyperbolic Time Chamber (精神と時の部屋, Seishin to Toki no Heya, The Room of Spirit and Time) is a place located on Kami's Lookout. Inside the Chamber time seems to pass very slowly, and there is a higher gravity level than Earth's - a step over the threshold of the training area brings one immediately into 10x Earth's gravity (the same as that of Planet Vegeta and King Kai's Planet), and the air gets denser the deeper one goes into the training area.
The Hyperbolic Time Chamber has an entrance at its center, located in a central building with two side wings with housing, food supplies, bathing quarters and sleeping quarters. There is no night or day in the Room, but the surroundings remain a constant bright iridescent white aurora. Its reflective floor is of undefined area, and the Room's boundaries are thought to stretch to infinity in all directions even though it appears to have a definite atmosphere, limiting its size. Goku explains to Gohan during their visit to the chamber that the air grows increasingly dense in the recesses beyond the plaza, which can be threatening as the Hyperbolic Time Chamber has no definite boundaries. The Hyperbolic Time Chamber represents a separate dimension from that of Earth.
The time dilation that occurs in the Hyperbolic Time Chamber is one day of real time is equivalent to one year in the Chamber, or 1 minute of real time is approximately six hours in the Chamber. There are dual giant hourglasses of emerald sand adorning the sides of the building that count down a year within the chamber. A clock on the dome roof of the main part of the building tells the applicable time in the real world.
This essentially allows for someone entering the Hyperbolic Time Chamber to get one year worth of intense training in a single day.
The gravity in the Hyperbolic Time Chamber living area is described as being "different", though it seems to not be much higher than Earth's gravity. The gravity of the training area is 10g. Gohan's first step over the threshold of the training area brought him to his knees; Trunks also had some difficulty with the gravity, but Goku and Vegeta were both well accustomed to much higher levels of gravity by the time they used the chamber.
The temperature in the training area fluctuates rapidly, and the air of the chamber becomes much denser the farther one goes into the training area. Goku, Gohan, Vegeta and Mirai Trunks are the only characters shown to go deep into the chamber. It isn't shown if Piccolo, Goten, or Trunks did, though it seems unlikely that any of the three would have much trouble with it.
The wooden door entrance is a portal between the Earth and the Hyperbolic Time Chamber, and is the only way to travel between the two dimensions without ripping holes in the dimensional walls.
The Chamber can only be entered twice by a person (or two days/years in total), as by the third time the door locks, leaving them in nothingness and not allowing anyone else to use the door. Also, there are only enough provisions to accommodate two people for the full year. This is commonly misinterpreted as a two-person limit overall, but it should be noted that in the Buu Saga four people in total entered through the main door. Vegeta and Trunks are the only two to enter the room for two entire days, though due to their lack of mastery of the Super Saiyan form, they increased far less than Goku and Gohan had in less than one year inside. Goten and Trunks are the last to train in the room when, upon Buu's transformation to Super Buu, Piccolo decides to give them time inside. In less than half of the hour (roughly one week inside the chamber) that Piccolo told Buu to wait, they achieve all three Super Saiyan levels.
Dragon Ball Z
Vegeta and his son Trunks enter the Chamber to train for their attempt to prevent Cell from attaining his complete form. Both train as ascended Super Saiyans, and Trunks surpasses his father in brute strength, but has issues with not getting in the way of his father's pride, so Trunks hides his power level. Trunks unknowingly makes a mistake by using his time in the Room of Spirit and Time to increase his strength, while sacrificing his speed and dexterity. Both Vegeta and Trunks fail to prevent Cell's completion, although Vegeta deliberately took part in allowing Cell to become complete for the sport of fighting him at a more challenging state.
Goku and his son Gohan enter the Chamber in preparation to fight against Cell. While training with his father, Gohan becomes a Super Saiyan, becoming the youngest Super Saiyan of his time. They both emerge from the Chamber with a heightened control over their Super Saiyan transformation. They developed an optimisation technique to stay in the Super Saiyan state for long periods of time in order to eliminate the strain from transforming. This allowed them to save energy for fighting, and worked so well they could even sleep while in Super Saiyan form. This training greatly assisted in Gohan's upgrade to Super Saiyan 2 during the Cell Games.
Piccolo entered the Chamber for meditation and self training, followed by Vegeta and Trunks entering again, increasing their power levels even further (although not quite surpassing Goku and Gohan). Piccolo reached a level of power equal to or possibly greater than Cell in his semi-perfect form (given he could hold his own against a Cell Jr., a much more powerful foe than "semi-perfect" Cell). Trunks and Vegeta's power levels didn't increase near as much as the first time they entered (possibly due to the fact that unlike last time, they acquired no new forms during this period, instead focusing on powering up their regular Super Saiyan state to its maximum), but they still improved enough to put up an evenly matched battle against the Cell Jrs. The Hyperbolic Time Chamber was not used again until after the Cell Games.
Goten, Trunks, and Piccolo enter the Hyperbolic Time Chamber to lure in the horrible Super Buu. When Buu enters the Room, Trunks and Goten use the Fusion Dance technique to become Gotenks. They introduce their Super Ghost Kamikaze Attack and upgrade themselves to Super Saiyan while fused. During the battle Gotenks falsely says he can't win in hopes of creating a more dramatic victory. Believing the act, Piccolo destroys the Room of Spirit and Time's entrance, leaving no way out. Buu can't stand the thought of being stuck in the Room (mostly because of his fondness towards chocolate, and the lack of it in this dimension). So Buu in an intense rage, screams at the top of his lungs. The scream is so loud, that it rips a hole leading back to Earth's dimension. Buu gets out but it's too late for Gotenks and Piccolo, as the portal closes behind him. Gotenks and Piccolo attempt to recreate Buu's mad howl, and succeed only after Gotenks transforms into Super Saiyan 3, and yells their way out.
The Hyperbolic Time Chamber is rendered non-functional without a door, and must be repaired for future use. It can be argued that when Buu destroyed the Lookout in later episodes, the Hyperbolic Time Chamber could have been fully repaired because the Lookout was wished back damage free.
The Hyperbolic Time Chamber is featured as a playable battle stage in the game Dragon Ball Z: Budokai Tenkaichi, and both of its sequels, where for the sake of playability, a transparent wall encloses the plaza (rather than the area surrounding it being infinite as it is in Dragon Ball Z). The time chamber, or rather, it's entrance/exit, also made a cameo in the barren planet stage of Dragon Ball Z: Burst Limit. In the video game, Dragon Ball Z: Sagas, it is used to train Gohan, Trunks and Vegeta to transform into Super Saiyans.