If a thyroid gland is enlarged and causing compressive symptoms, there is a concerning nodule or it is producing too much thyroid hormone that can't be controlled with medication then it can be removed surgically.  Depending on the reason for the operation, this may require removing part or all of the thyroid gland.  You will need to stay overnight in the close observation unit after the operation and are usually able to go home the day after surgery.

Read about thyroidectomy here.