Read the two numbers together. A low T4 tells you there is too little thyroid hormone, and a high TSH tells you the pituitary is shouting at the thyroid to make more. When the controller (pituitary, via TSH) is clearly active but the output hormone (T4) is still low, the failure must lie downstream, in the thyroid gland itself. That defines primary hypothyroidism.
This single observation eliminates the central causes. If the problem were pituitary failure or hypothalamic failure, the gland would not be receiving its signal, so TSH would be low or inappropriately normal alongside the low T4, not high. A high TSH proves the pituitary axis is intact.
It also eliminates Graves disease, which is the mirror image: an overactive thyroid with high T4 and suppressed TSH. The remaining and by far the most frequent cause of a failing thyroid in an iodine replete population is autoimmune Hashimoto thyroiditis, in which antibodies progressively destroy the gland.\[\boxed{\text{Hashimoto's disease}}\]