The Peekaboo module is designed to allow a field's full formatted value to not be calculated and output during a page load of the node, but to be pulled in through a separate request.
This was to reduce overhead in the contents of 'reference' modules such as Node reference, or View reference, which can potentially require the usual field formatter to do quite a lot of work, such as loading several nodes. Peekaboo is particularly useful when the references are nested, and can allow the user viewing the node to 'drill down' through the references with several Ajax requests.
The design of Peekaboo was changed between 6.x-1.x and 7.x-2.x. In 6.x-1.x Peekaboo uses a CCK field which acts as a sort of "field reference" to the field you want to include with Ajax. As of 7.x-2.x Peekaboo is purely a field formatter, and the removed functionality is now part of Field reference.
The following pages contain documentation about the Peekaboo; Ajax field formatter.