Med-X addiction is a form of addiction which can occur in Fallout 3 and Fallout: New Vegas.
You used the chem Med-X once too often and now your body is craving for more... and more... and more... well done! You got yourself addicted.
When addicted to Med-X, you suffer from a -1 penalty to Agility and Intelligence.
In Fallout: New Vegas during the quest Bye Bye Love, a Medicine check allows the player to tell Joana that her 'contracted pupils and involuntary spasms' are signs of Med-X addiction.