The Collaborative International Dictionary of English v.0.48:

grommet \grom"met\ (gr[o^]m"m[e^]t), n. [F. gourmette curb, curb
   chain, fr. gourmer to curb, thump, beat; cf. Armor. gromm a
   curb, gromma to curb.]
   1. A ring formed by twisting on itself a single strand of an
      unlaid rope. Sometimes written grummet.
      [1913 Webster]

   2. Any eyelet or ring of metal or other material inserted in
      a hole in a sheet of some other material; in sailing, a
      metallic ring in or for a sail or a mailbag.
      [1913 Webster]

   3. A ring of rubber or other insulating material inserted in
      a hole in some surface of a device, to prevent wires
      passing through the hole from making contact with the
      surface; used especially in electrical and electronic
      devices, to prevent undesired electrical contact.
      [PJC]

   4. (Mil.) A ring of rope used as a wad to hold a cannon ball
      in place.
      [1913 Webster]

WordNet (r) 3.0 (2006):

grommet
    n 1: fastener consisting of a metal ring for lining a small hole
         to permit the attachment of cords or lines [syn: cringle,
         eyelet, loop, grommet, grummet]

Moby Thesaurus II by Grady Ward, 1.0:

32 Moby Thesaurus words for "grommet":
   air hole, annulet, armhole, blowhole, bullet-hole, bunghole,
   circlet, cringle, deadeye, eye, eyelet, gasket, guide, keyhole,
   knothole, loop, loophole, manhole, mousehole, peephole, pigeonhole,
   pinhole, placket, placket hole, porthole, punch-hole, ringlet,
   roundlet, spiracle, tap, vent, venthole