How do the <sight> tag and its various arguments work?

In monster definitions, how do the <sight> tag and its various arguments ("cone", "modifier") work?

 

Cone can be 90, 180, 270, or 360 (only sees things in front of them; sees things in front and somewhat on the side; sees everything that is not behind them; sees everything, and the value is in degrees, 90 being a quarter of a full disk, 180 being half of it, and so on.
And the higher the modifier, the higher their chance to detect you is, and it can have values from 0 to hell-knows.