Hyperbaric oxygen therapy (HBOT) involves breathing oxygen in a pressurized chamber in which the atmospheric pressure is raised up to three times higher than normal. Under these conditions, your lungs can gather up to three times more oxygen than would be possible breathing oxygen at normal air pressure (from the FDA).
Hyperbaric chambers are medical devices subject to FDA approval. HBOT has not been approved for use in autism (or most of the other conditions it is purported to treat). This means HBOT has not been clinically demonstrated to be a safe and effective treatment for autism. As with many treatments, the claims made regarding the effectiveness of HBOT are not grounded in evidence.
HBOT is approved by the FDA for thirteen conditions, including air or gas embolism, carbon monoxide poisoning, decompression sickness and burns caused by heat or fire. While off-label use (the use of a drug or medical device for an indication other than what it is approved for) is not necessarily a problem, it does demand a higher level of scrutiny in considering the risks and benefits of the off-label use.