Grommets and eyelets are metal, plastic, or rubber rings that are inserted into a hole made through another material. They may be used to reinforce the hole, to shield something from the sharp edges of the hole, or both.
Grommets as reinforcement
Grommets are used to reinforce holes in leather, clothing, shoes, and other fabrics. They can be made of metal or plastic, and are easily used in common projects, requiring only the grommet itself, a grommet-setting tool (a metal rod with a convex tip which usually comes with the grommets when you buy them in a store), and a hammer. Fancier grommet presses (as shown in the picture) exist but generally a hammer and the grommet-setting tool works at least as well for setting just a few grommets. Their most common usage is to strengthen the holes for bootlacing but are also good for making corsets and other laced clothing, plus curtains and other household items that require hanging from hooks. The grommet prevents the cord from tearing through the hole and thus provides structural integrity. Small grommets are also called eyelets, especially when used in clothing.
Grommets used as shielding
If metal or another hard material has a hole made in it, the hole may have sharp edges. Electrical wires, cord, rope, lacings, or other soft material passing through the hole can become abraded, resulting in failure. Instead, a rubber or plastic grommet can be inserted into the hole and the wire (etc.) passed through the grommet. The soft texture of the grommet shields the wire from damage. This is very commonly done wherever wires pass through punched sheet metal and rubber grommets are manufactured in a wide variety of sizes expressly for this purpose.
A grommet can also be a small teflon tube inserted into the eardrum to allow air to pass through it into the middle ear to alleviate the hearing loss and pain that can occur with repeated ear infections, a condition sometimes known as glue ear. This is also a correcting measure for a patulous eustachian tube, when air moves to and from the middle ear with each breath making the eardrum flap.