Bandhas literally means to join together, to tie or to contact or to hold or to lock. Basically, it is a process of controlling of prana through series of muscular contracts which activate nerves and endocrine system. These bandhas activates three energy centers such as mooladhara linked with swadhisthana, manipura linked with anahata and vishuddhi linked with ajna.
Moolabandha - It is done by contracting the anus muscles [ to draw the apana vayu upwards]. It is meant for activating the mooladhara chakra (root of all energy centres) and the position of this chakra is between the reproductive organ and anus. Remember these energy centres or chakras in yogic texts are physically visible in the physical body; these are in our pranic body. The practice of this bandha helps yoga aspirant to keep up celibacy - controls sex hormones and relieves one of constipation. This bandha may also practiced while bhujangasana, ustrasana, dhanurasana and paschmitonasana.
Helping Mudra - Ashwani mudra.
Uddiyana Bandha: It is said that by practising and mastering this bandha, the prana flies upwards through sushumna nadi. It is done by fully and effortful exhalation and contracting the abdomen in such it rests against the back of the body high up in the thoracic cavity - exhale and contract abdomen inside so that it is touched with the back and hold, as per the stamina and capacity. It helps in celibacy as well as constipation, weak intestines and other digestive orders.
Nauli kriya starts with this bandha. This shall be discussed later on.
Helping Exercise : Agnisara.
Jalandhara Bandha: Contract the throat and press the chin firmly against the chest. It is said that the jatharagni or digestive fire which is situated in the region of navel consumes the nector which is released from the Sahasrara Chakra through the hole in the palate in the skull. This bandha prevents the nectar being thus consumed. Physiologically, it helps regulation of blood circulation, removes congestions of nasal passage and activates thyroid and parathyroid glands.
You asked one question about yoga for thyroid, one can do this bandha for good results but with precaution as follows:
Contraindication: Heart patient and high blood pressure, cervical spondilytis.
There is another bandha which is called Mahabandha which is combination of the all above bandhas. One should practice this one only after one masters all the above individually. First moolabandha, then uddiyana bandha and then jalandhara - sit in sukhasana or comfortable posture and then contract anal muscles upwards and breathe out breath slowly and hold and draw your abdomen inside and then press the chin firmly against the chest. This should be done below your capacity and not beyond your capacity; else it may harm you. I may remind that asanam sukham sthiram - pay attention to the stability and comfort.
Generally, it is said that the yogi achieves all his desiers and obtains siddhis, as it opens higher centres of the brain.