Look closely at a brake rotor and you will usually find a number stamped or cast into it - the minimum thickness, sometimes marked "min th" or "discard." It is one of the most important brake specs, because it decides whether a rotor is still safe to use.
What minimum thickness means
Rotors wear thinner over their life as the pads grind against them. The minimum thickness is the point below which the rotor can no longer safely do its job. A rotor thinner than that spec must be replaced - not resurfaced, not run a little longer. It is a hard safety limit set by the manufacturer.
Why a too-thin rotor is dangerous
A rotor's mass is what absorbs and sheds braking heat. A rotor worn below minimum has less material to soak up that heat, so it runs hotter, is more prone to warping and cracking, and can fade or fail under hard braking. Thin rotors also flex more, which can feel like a pulsing pedal. See warped rotors.
How it decides resurface vs replace
Resurfacing (turning) a rotor removes a thin layer of metal to make it flat and smooth again - which makes the rotor even thinner. A shop measures the rotor and will only resurface it if there is enough material to stay above minimum thickness afterward. Because many modern rotors start thin to save weight, there is often not enough margin to cut, so replacement is the common and affordable choice. See when to replace rotors.
The takeaway
Never install new pads against a rotor that is at or below minimum thickness - you would be building a fresh brake job on an unsafe foundation. When you replace rotors, do them in axle pairs and fit new pads and hardware at the same time.