The Hyperbaric Chamber is a device with medical properties manifested through the use of oxygen at a level higher than atmospheric pressure.
After Michael Peterson was found in the site of the explosion that took place during Agent Phil Coulson's kidnapping, the Centipede Project outfitted him with a Backscatter X-Ray Eye Implant, treated his wounds within an Hyperbaric Chamber, and was sent within the chamber to Italy.
He was awakened by Ian Quinn, and outfitted with a Cybertek Prosthetic Leg to begin working as a Centipede operative. Skye witnessed Peterson's awakening, and was shot shortly after by Quinn and left for dead.
When her team raided the compound, Coulson found her barely alive after a massive blood loss. Agent Jemma Simmons ordered to put her into the chamber to stabilize her condition, and she was transferred to the Bus inside the Chamber to keep her alive. 
Inside the Hyperbaric Chamber, Skye was taken to S.H.I.E.L.D. Trauma Zentrum, where Dr. Jazuat stated that Skye would not have survived till she was able to get into surgery without the machine. However, despite her best efforts, Dr. Jazuat informed Skye's teammates that she would not be able to save her. Skye was then returned to status within the chamber and transferred via Medical Pod to the Bus and taken to the Guest House. 
After Jemma Simmons and Leo Fitz came up from being trapped ninety feet below the Atlantic Ocean, they were saved by Nick Fury. They were placed in hyperbaric chambers in order to compensate for the depressurization.