FITS stands for FAA-Industry Training Standards, which is a modern training program created by the FAA in order to address the need for change in flight training practices recently.
In 2003, the FAA set out to modernize flight training methods after a number of technologically advanced aircraft (TAA) hit the market. The advanced avionics systems in these new aircraft require a certain diligence from pilots. The current flight training standards were created in 1973, and don't address cockpit management in a meaningful way. The influx of TAA meant that student pilots would be flying the same (if not more modern) systems than airline and corporate pilots, yet they weren't trained properly for that type of flying.
The FAA decided that rather than introduce a new set of regulations, which would make flying even more restrictive and expensive than it is already, they would implement a completely voluntary system within the flight training community that addressed the need for updated training standards. This new system was called FITS.
FITS is not mandatory -- only highly encouraged. The FITS program takes flight training from a manuevers-based philosophy to a scenario-based training (SBT) method. The idea is that by incorporating real-world scenarios into training, students will improve upon decision-making and judgment skills and become an active participant in the training environment. The FITS program is meant for use in TAA training programs, but can be used for any non-TAA program as well.
There are three elements to a FITS program: Scenario-based training, single-pilot resource management and learner-centered grading. These concepts are meant to enhance the FAA's existing syllabi standards, not replace them.
The FAA didn't work alone in creating the FITS programs. Collegiate universities and other professional pilot programs, along with other industry players, assisted with the research and development needed for the FITS program to take flight.