DIAGNOSIS That's usually the sound of the print head carriage trying to move but hitting an obstruction or moving on dried ink. It's a distinctive metal-on-plastic grinding or crunching sound.
FIX Turn the printer off immediately. Open the front cover where the cartridges are. Look inside at the black plastic rail that the print head moves on. You'll probably see blobs of dried ink or dust. Take a cotton swab lightly dampened with distilled water (or a tiny bit of isopropyl alcohol) and wipe that silver rail clean. Also, wipe the flat plastic guide next to it. Make sure there's nothing like a paperclip or torn label stuck in there. Manually slide the print head carriage from side to side—it should move silently and freely.
IF THAT DIDN'T WORK The obstruction might be under the carriage. Shine a flashlight under the print head carriage itself. If you see a thick buildup of ink, carefully clean it with a damp swab. Also, check for any bits of paper from a past jam caught in the mechanism.
HEADS UP Never force the carriage if it's stuck. You can strip the gears on the motor. If cleaning the rail doesn't fix it and the noise persists, the carriage motor or encoder strip might be failing, which is a more serious repair.