The Prescription Drug User Fee Act (PDUFA) is a law enacted by Congress that gives powers to the FDA.
Amongst other things the law allows the FDA to charge drugmakers to review their New Drug Applications or Biologics License Application. The FDA uses this money to speed up the review process. A typical review time is 10 months for a standard review or six months for an expedited review. The term "PDUFA date" comes from these waiting times, but is not really a deadline; the FDA tries to complete its review by the PDUFA date, but has handed down its ruling after the PDUFA date many times.
The version signed into law on September 27, 2007, was the fourth iteration of PDUFA and gave the FDA more powers to review the safety of drugs after marketing approval.