You can essentially look at TSH to the thyroid as you would LH to the testes and testosterone. Both are secreted in the pituitary and designed to prompt, or call it signal the production of their respective hormones via the negative loop feedback. This is a great setup "when" it works! However, for a myriad of reasons most of us know that sometimes it just doesn't work as it should.
The pituitary can stop producing a "normal" amount of LH, thus secondary hypogonadism sets in. Introduce exogenous testosterone, your serum levels increase, which will cause LH to pretty much stop all together.
Same is true with TSH < ------------> Thryoid -> T4, T3, T2, T1 ... Add an exogenous source (could be Synthroid, Cytomel, NDT, ...), the pituitary will register that as "thyroid hormone levels increased", this in turn prompts the pituitary to reduce TSH "stimulation hormone".