Abnormal function. When the thyroid gland produces too much thyroid hormone (becoming overactive), the condition is called hyperthyroidism. When the thyroid gland produces too little thyroid hormone (becoming underactive), the condition is called hypothyroidism.The most common cause of hyperthyroidism is an autoimmune condition called Graves' disease.bnormal function. When the thyroid gland produces too much thyroid hormone (becoming overactive), the condition is called hyperthyroidism. When the thyroid gland produces too little thyroid hormone (becoming underactive), the condition is called hypothyroidism.