In endocrinology, this works almost as a law: If something is low, stimulate the gland. If it is high, suppress the gland. This helps with diagnosis.
Stimulating a gland (e.g. the adrenal glands) when the hormone it produces (e.g. cortisol) is low allows you to know if the problem lies with the gland itself or with a lack of the hormone that stimulates that gland to produce (e.g. ACTH in the case of the adrenal cortex).
In the case of the adrenal gland, ACTH stimulation test = Cosyntropin stimulation test.
Dexamethasone suppression test is used to test the status of the hypothalamic-pituitary-adrenal (HPA) axis when faced with high levels of adrenal hormones (adrenal hyperfunction).