The Zero Room was an important room in the the Doctor's TARDIS (and presumably of other models of TARDIS).
Zero Rooms were used by the Time Lords in times of difficult regeneration or to rapidly heal. It was cut off from the random electrical and radiological influences of the rest of the universe. It was ideal for neurological healing. (CC: The Invasion of E-Space) It had a calming, restful atmosphere. As the Doctor demonstrated to his companions, some physical laws had not as much influence here as in the rest of the universe. For instance, he could levitate here at will. (DW: Castrovalva)
When the First Doctor wanted to rest and contemplate, he used the Zero Room. (ST: The Rag and Bone Man's Story)
Romana put the Fourth Doctor in the Zero Room after he recieved damage to his synapses. (CC: The Invasion of E-Space)
The Zero Room was used by the Doctor following the regeneration of his fourth incarnation. The destruction of the Zero Room came about when the TARDIS needed to eject part of its structure to generate power in order to break free of Event One. Nyssa, however, used tools to cut the walls of the room and from them, construct the Zero Cabinet which had the same properties. Nyssa and Tegan found the cabinet light enough to carry, in part because the Doctor used levitation to negate his own weight. (DW: Castrovalva)
Later the Zero Room was reconstructed in the TARDIS. (BFA: Renaissance of the Daleks) The Sixth Doctor used it to stabilise Charley when she was sick. (BFA: Patient Zero)