The Accounting Department is a location within the Neutral Zone which calculates the value of each and every human's life. When a human's life is completed, that human's file is sent to the Good or Bad Place (depending on which place the human will go to) so that the Architects can design a Neighborhood that will reward or punish them.
The Accountants are a type of Immortal Being whose purpose is to calculate the total value of each human life and determine whether that human should be sent to the Good or Bad Place.
Their main purpose seems to be to calculate the value of new actions rather than the value of human lives themselves, as those are recorded in Books, which appear to contain every human with identical first names and their files.
Doug Forcett stated in Chapter 35: Don't Let The Good Life Pass You By that individual accountants measured the value of individual human lives themselves. It is unknown, if there are additional accountants who perform this action, or if this was part of the 8% of the afterlife that he guessed incorrectly.
The Head Accountant, Neil, supervises the Accounting Department and has complete access to all of the information about every human value. He seems not to have a job in calculations whatsoever, but does supervise his employees, as seen when Matt requests immediate suicide, which Neil denies.
All of the information about human actions on Earth are sent to a main feed in the center of the Accounting Office. If the action is a new action that has never been done before (99% of which, according to Neil, are categorized as Weird Sex Things) is then distributed to the relevant accountants (each of whom deal with a certain type of action), and they calculate a point value for the action, which is then randomly checked by three billion different accountants simultaneously. The actions are then sent to the relevant Books.