A grommet is a small circle of metal that protects a hole meant for threading a cord or cable through. You lace up your favorite boots by threading a shoelace through grommets.
The eyelets on your shoes are just one type of grommet. The metal rings at the top of a shower curtain that connect to the sliding hooks on the rod are also grommets, as are the reinforced holes in a sail meant for threading ropes through. Holes in sheet metal often have grommets to protect cords and cables from being cut on the sharp metal. A grommet, which was originally "a wreath of rope," is a useful gadget.