The Collaborative International Dictionary of English v.0.48:

Pare \Pare\, v. t. [imp. & p. p. Pared; p. pr. & vb. n.
   Paring.] [F. parer to pare, as a horse's hoofs, to dress or
   curry, as, leather, to clear, as anchors or cables, to parry,
   ward off, fr. L. parare to prepare. Cf. Empire, Parade,
   Pardon, Parry, Prepare.]
   1. To cut off, or shave off, the superficial substance or
      extremities of; as, to pare an apple; to pare a horse's
      hoof.
      [1913 Webster]

   2. To remove; to separate; to cut or shave, as the skin,
      rind, or outside part, from anything; -- followed by off
      or away; as, to pare off the rind of fruit; to pare away
      redundancies.
      [1913 Webster]

   3. Fig.: To diminish the bulk of; to reduce; to lessen.
      [1913 Webster]

            The king began to pare a little the privilege of
            clergy.                               --Bacon.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Paring \Par"ing\, n. [From Pare, v. t.]
   1. The act of cutting off the surface or extremites of
      anything.
      [1913 Webster]

   2. That which is pared off. --Pope.
      [1913 Webster]

            Pare off the surface of the earth, and with the
            parings raise your hills.             --Mortimer.
      [1913 Webster]

WordNet (r) 3.0 (2006):

paring
    n 1: a thin fragment or slice (especially of wood) that has been
         shaved from something [syn: paring, sliver, shaving]
    2: (usually plural) a part of a fruit or vegetable that is pared
       or cut off; especially the skin or peel; "she could peel an
       apple with a single long paring"

Moby Thesaurus II by Grady Ward, 1.0:

118 Moby Thesaurus words for "paring":
   afterglow, afterimage, balance, bit, bones, butt, butt end,
   candle ends, chaff, chip, chunk, clip, clipping, collop, crumb,
   culm, cut, cutting, dandruff, deadwood, debris, detritus,
   dishwater, dollop, draff, dregs, dust, end, fag end, filings,
   flake, floccule, flocculus, flock, fossil, fragment, garbage, gash,
   gob, gobbet, hogwash, holdover, hunk, husks, leavings, lees,
   leftovers, lump, modicum, moiety, morsel, odds and ends, offal,
   offscourings, orts, parings, particle, piece, potsherds, rags,
   rasher, raspings, refuse, relics, remainder, remains, remnant,
   residue, residuum, rest, roach, rubbish, ruins, rump, sawdust,
   scale, scoop, scourings, scrap, scrap iron, scraps, scum, scurf,
   shadow, shard, shards, shaving, shavings, shiver, shred, slack,
   slag, slice, sliver, slop, slops, smithereen, snack, snatch, snip,
   snippet, splinter, stitch, straw, stubble, stump, survival,
   sweepings, swill, tares, tatter, trace, vestige, wastage, waste,
   waste matter, wastepaper, weeds