It's a test used in an exam of neurological function for balance.
It is used to diagnose problems with balance, which is composed of visual, vestibular (inner ear), and proprioceptive (positional sense) systems during a neurological exam.
A positive Romberg test denotes sensory ataxia (loss of coordination) as the cause of postural imbalance.
This test is used to determine if proprioceptive impulses are being transmitted up the spinal cord to the brain properly.