Pull a wheel and find deep grooves cut into the rotor face and you are looking at rotor scoring. Light scoring is normal wear; deep scoring means something went wrong. Here is what causes it and when the rotor needs replacing.
Worn-out pads (metal-on-metal)
The most common cause of heavy scoring is running the pads until they are gone, so the steel backing plate or the pad's rivets cut into the rotor - see why brakes grind. This carves deep grooves fast and is why you should not run pads to zero - see minimum pad thickness. Metal-on-metal scoring often ruins the rotor.
Trapped debris
Grit, sand, or a small stone caught between the pad and rotor acts like a cutting tool, scoring a groove until it clears. A bit of debris scoring is common and usually shallow. Rust chunks from a badly corroded rotor or heavy road grime can do the same, especially after the car sits.
Embedded material or a hard spot
Foreign metal embedded in the pad, or a hardened hot spot on the rotor, can score the mating surface as it rotates. Contaminated cheap pads sometimes carry hard inclusions that scratch the rotor.
When scoring means replace
Light scoring (fine lines you can barely catch a fingernail on) is normal and fine. Deep grooves you can feel, or scoring past the point where resurfacing would leave the rotor below minimum thickness, mean replace it - see resurface vs replace and when to replace rotors. Fit new rotors as a pair with quality pads and fresh hardware.