A short and snappy summary:
Hormones are typically produced by the endocrine system, which includes the following group of glands and the pancreas: pituitary, pineal, thymus, thyroid, and adrenal.
Your gut microbiome also produces hormones, and in addition, sends signals to the glands in your body that dictate how much of each specific hormone we release.
Gut dysbiosis (an imbalance of good and bad bacteria) can lower the levels of thyroid hormones T3 and T4, which can lead to what's called hypothyroidism (where your thyroid gland doesn't produce enough hormones). Symptoms include "tiredness, weight gain, dry skin, cold intolerance, constipation, muscle weakness, puffiness around the eyes, hoarse voice, and poor memory.". (study)
So much like our immune system, that ecosystem of microbes in your gut are affecting our hormones. Who'd have thought what many see as just our "stomach" had such a widespread influence...