We are born with a ring of tissue in the back of the throat made up of the tonsils (at the side of the throat which look like wallnuts and can vary in size) and the adenoids (above the soft palate and not visible without special instruments). They are the first line of our immune system where foreign material is caught and the body learns to defend against these bugs.
By the age of about 3 the tonsils and adenoids start to be absorbed. If this does not happen then they can cause obstruction which can manifest from light snoring to full blown sleep apnea. Enlarged tonsils and adenoids are thus removed surgically.
The adenoids can lead to a second common problem and that is glue ear as they obstruct the Eustachian tube leading to an accumulation of fluid in the middle ear.
Another big group of patients who undergo a tonsillectomy are those who get recurrent infections and thus are often on antibiotics with all the side effect they bring. If the tonsils are removed then the most common locus for bacteria is also removed resulting in less frequent infections and antibiotic use.