Enlarged thyroid. Goiter (GOI-tur) is an abnormal enlargement of your thyroid gland. Your thyroid is a butterfly-shaped gland located at the base of your neck just below your Adam's apple.Although goiters are usually painless, a large goiter can cause a cough and make it difficult for you to swallow or breathe.nlarged thyroid. Goiter (GOI-tur) is an abnormal enlargement of your thyroid gland. Your thyroid is a butterfly-shaped gland located at the base of your neck just below your Adam's apple.