What does the diagnosis "hyperthyroidism secondary to graves' disease" mean in layman's terms?

See below. It means graves' disease is the cause of your hyperthyroidism. Hyperthyroidism just means you have too much thyroid hormone. There can be several reasons for that; graves' is one of the common ones.
Graves disease. It means you have graves disease causing your thyroid to produce too much hormones. It doesn't go away on its own and will need to be treated.