2000 Jag S-Type 3.0 note flashes on the dash"engine Fail Safe Mode" What does that mean?

Typically when a newer vehicle goes into a failsafe (some companies call it limp-home mode) it is because the on board diagnostics system is sensing a problem with the engine operations. however, typically when a car goes into a limp mode, they make very little power, only enough to literally limp the car somewhere safe. If you have had any sort of mechanical problems recently, I would take up your issue with whomever fixed it before. Also, if you do not keep up with regular maintenance, I would check through the manual and see if there isnt some issue that jaguar feels is a "must" item to repair/replace periodically.

Failense engine mode