I'm curious to know what they actually do. Do we risk the locking of this thread, or do I scar my eyes by looking at google images?
What they do varies.
In general, though, and in the most clinical terms possible, the clitoris and its hood are excised, and sometimes parts of the labia. The most extreme cases include complete removal of the clitoris and hood, complete removal of the labia minora, and removal of the skin from the inner sides of the labia majora. The exposed meat is then stitched together - sometimes using thorns - and the girl's legs are bound together. When the wound heals, the external genitalia are almost completely missing, as the labia majora have healed together and are almost completely closed. This accounts for about 10% of the procedures performed in those cultures where this is considered normal.
Occasionally, rather than excision, the offending features are simply cauterized, burned away.
So, like I said, it's about a billion times worse than male circumcision.
It's done to enforce chastity. It's done to girls when they are very young, but still old enough to understand what's happening.
I strongly recommend against looking for pictures.