Your brakes have started grinding and you are wondering if it is safe to keep driving to get it fixed later. The honest answer for most grinding is: no, not safely. Grinding is one of the more urgent brake noises. Here is why and what to do.
What grinding usually means
A harsh, low grinding - especially one you feel through the pedal - typically means the pads are worn completely away and the steel backing plate is now cutting into the rotor, metal-on-metal; see why brakes grind. At that point braking power is reduced and dropping, and every stop does more damage.
Why it is urgent
Metal-on-metal braking is both less effective and rapidly destructive. You are grinding grooves into the rotor (turning a pad job into a pad-and-rotor job), and stopping distances lengthen - dangerous in an emergency. In the worst case it can damage the caliper too. A grinding brake is a fast-worsening safety problem, not a wait-and-see one.
The exceptions
Not every grind is worn-out pads. A brief grind on the first cold or wet stops that clears immediately is usually harmless surface rust - see brake noise after sitting. A one-time light scrape from a stuck dust shield is cosmetic. But a steady grind that stays or is felt in the pedal is the dangerous kind.
What to do now
If the grinding is constant or felt in the pedal, stop driving and have it inspected - drive only the minimum to get it serviced, or have it towed. You will likely need pads and possibly rotors; see minimum pad thickness. Replace with quality pads and fresh hardware right away.