The quick answer is that when a person is in a hyperbaric oxygen chamber, the increased pressure surrounding them forces the oxygen that is breathed in to be dissolved into the plasma portion of the bloodstream.

It helps to understand the basic components of the bloodstream and their function:

The major components of the bloodstream are red blood cells, white blood cells, platelets, and plasma.

Under normal conditions, when a person breathes oxygen into the lungs, red blood cells in the bloodstream pick up and carry oxygen molecules, making them available to all parts of the body. Generally, about 95 percent of the red blood cells (hemoglobin) are carrying oxygen molecules at any one time. 

• White blood cells (leukocytes) are part of the body’s immune system and help keep foreign bodies (allergens, bacteria, viruses, etc.) under control, or help to clean up dead cells or waste by-products produced by our cells. 
• Platelets help the blood to clot, springing into action when we have a cut or injury. They help staunch the flow of blood leaking out of broken or torn blood vessels. 
• Plasma is the watery fluid that constitutes over half of the volume of our blood.  Dissolved in it are nutrients and vitamins, electrolytes, hormones, clotting factors, proteins, fats, sugars, metabolic wastes and other substances. The other blood cells (red, white and platelets) float in the plasma as it is circulated through the body. Unlike the red blood cells, the plasma seeps from the blood vessels into spaces between cells, carrying nutrients with it, and picks up waste by-products for later disposal. Plasma is the clear fluid that seeps out when someone has a minor skin scrape or brush burn.

The red blood cells are the most common cell type in the bloodstream, but the plasma has the most volume.

When a person is in a hyperbaric oxygen chamber:

• Oxygen molecules are dissolved into the plasma. 
• Oxygen levels are increased only slightly in the hemoglobin (RBC), which is already working at about 95 percent capacity. 
• The bloodstream can carry as much as six times more oxygen than while breathing room air outside of the chamber. 
• The plasma is infused with enough oxygen to sustain life without any hemoglobin. 
• This oxygen-saturated plasma moves from the circulatory system into tissue spaces, seeping into areas where there is no blood flow, or where blood flow is diminished or compromised and carries oxygen molecules with it. More oxygen is delivered to more cells than can be delivered by the circulatory system.
• There is less energy transfer involved when a cell receives an oxygen molecule.
• Other body fluids, such as the cerebrospinal fluid, are also infused with molecular oxygen.
• The total effect is that the body has become hyperoxygenated and thus, the process is known as hyperbaric oxygenation. 

Breathing 100 percent oxygen under pressure enhances a body’s ability to heal itself naturally.