Hi Lilly,
I used to get those alot when I was a small child. I did a quick search on google and came up with some of the follwing info. I hope is helpful to you: "The little white particles are called tonsilloliths and except for their bad smell are not a condition to be worried about. Tonsilloliths form when mucus, bacteria, and debris condense into small particles on the surface of the tonsils. These odorous balls of material are sometimes coughed up."
"There are deep holes in the tonsils, known as crypts. These holes are supposed to be there, they provide areas where the good white cells of the body can fight the bad bacteria. Then the dead bacteria and dead white cells are extruded and swallowed. Sometimes the holes are too wide or crooked and the material gets to accumulate and cause odor. 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. 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. "

Woops...sorry...it is getting late here and I am tired. I just realized you didn't want to know WHAT it is but HOW to get rid of it. If seems besides extracting them manually which can cause the tonsils to bleed sometimes, you can try irrigation which can be done w/ a waterpik with special attachments (see below) Good luck! ;o)

"Irrigation of the throat is shown to bring blood to the area, encourage lymphatic drainage, and remove bacteria on the surface and in the crypts.
Washing away surface bacteria helps reduce the number of bacteria that the body has to fight. Bringing more circulation to the area means more natural white cells to kill the bacteria. More circulation means more dilution of the bacteria. This can be accomplished nicely by using pulsating irrigation to the throat, with the Hydro-Med throat irrigator tip. Pulsating irrigation is 100 times more effective than simple rinsing. By crow-barring out the bacteria, the body has its best chance of overcoming infection without Antibiotics .
Instructions for Use: Add saline or diluted Listerine or your favorite mouthwash to the Water Pik(TM) basin. The throat tip is concave to lay on the tongue comfortably.
Lay the tip straight back on the left side of the tongue and direct it just behind the last tooth. The stream will wash the left tonsil or side of the throat, come around and wash the other side.
Turn the tip over and wash the right side; again make sure the tip is on the right tongue straight back aimed for behind the right last tooth. About a minute on each side should be enough. Lower pressure is best."

http://www.ent-consult.com/throat_irr_use.html