Preflighting is a term derived from the airline industry. The pilot has the responsibility to determine the airworthiness of the aircraft before take-off. This means that he or she has to perform a number of checks prior to each flight.
Preflighting PDF documents basically means the same thing: the "pilot in command", i.e. the person who creates or processes a PDF document, has to make sure that the document is "airworthy", or rather, "outputworthy", before sending it for output.
"Outputworthy" means that the PDF document is "fit for use", for example:
Moreover, properties of a PDF document which do not meet the requirements of the preflight check can be reported as a "problem" and fixed in the same process.