Our brains are totally dependent upon blood and oxygen. One of the ways that you can suffer a brain injury is to deprive oxygen flowing to the brain. We call that a hypoxic brain injury.
Sometimes this type of brain injury can be minor where the brain for whatever reason is denied oxygen for several seconds but after several minutes brain cells begin to die. Drowning is a classic example but it can also occur in the context of medical malpractice cases where there is some mistake made and the person doesn't get the oxygen they need.
Many times when the oxygen is restored it will tend to minimize the damage that's been done. The brain will tend to recover but when you reach that point of no return, when the oxygen is deprived long enough, many times the function of the brain cells that have died will not recover. Whether that's memory or motor function, it can affect different areas of the brain and that is a very serious, and often permanent condition.