These are called tonsilloliths (or tonsilliths, as I so affectionately nicknamed them). They are the result of bacteria and food particles that get stuck in the pockets of your tonsils. This condition is totally harmless and commonly occurs in children and young adults, but also in adults. The only real cure is to have your tonsils removed, but this is costly, often unnecessary and can be a threat to your health, since your tonsils help to guard the body against bacteria. They stink. But you can live with it. I just push them out with my finger or the blunt end of my toothbrush. Here is the best medical/scientific explanation I've found:
"What are tonsil stones?
The tonsils usually appear like small, dimpled Golf balls set on either side of the back of the throat. Children with large tonsils and deep crypts often get food particles trapped in there. Because saliva contains digestive enzymes, trapped food begins to break down. Particularly, the starch or carbohydrate part of the food melts away, leaving firmer, harder remains of food in the tonsils. This does not look like the food that went into the mouth.
There is more to these hard lumps than just food. The tonsils also trap other mouth debris such as bacteria and old cells from the surface of the mouth's lining. Some of these cells contain small amounts of keratin, the same substance found in fingernails and rhinoceros horns. Whatever the nature of the debris, it is then attacked by white blood cells. The aftermath of this battle leaves the crevices of the tonsil strewn with hardened remains.
Most people swallow this material without ever noticing it, while it is still tiny. In those whose tonsils are large, however, the particles can lodge in the deep crypts, where they continue to grow. The enlarging lumps are called calculi of the tonsil, or tonsilloliths (tonsil stones). These stones are most common during adolescence.
Microscopic studies of these tonsilloliths have shown them to contain a combination of food particles, bacteria, oral debris, and white blood cells in a concentrically laminated pattern -- rather like a pearl. Usually they are small gritty particles found in the center of soft, cheesy flecks. Sometimes, however, they become quite large, appearing as rough, yellow or gray, round stones. At times they reach an extraordinary size. Affected people usually have a history of repeated attacks of tonsillitis in earlier years.
Alan Greene MD FAAP
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It's most likely a sign of a bacterial infection on your tonsils. This might be a sign that you have tonsillitis and you could get it checked out by a doctor for an antibiotic.
There are also things called tonsilloliths or tonsil stones. These are white matter that shows up in the tonsillar crypts which are holes in the tonsils.
White papules on the tonsils are usually pus, and often indicate an infection such as strep.
If you have white spots on your tonsils you probably have strep throat. The white spots are actually puss. See a doctor, get an anitbiotic and they will be gone in a day or two.