I believe this refers to the design element where animals, or some sort of tree branches or something like that supports the shield of the heraldic coat of arms.

The following website has a nice diagram with names for all of the elements of the coat of arms.

http://www.fleurdelis.com/coatofarms.htm

"supporters: usually two animals, birds or persons, appearing on either side of the shield."

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Note added at 1 hr (2010-05-19 16:18:57 GMT)
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Wikipedia has a similar schematic:

http://en.wikipedia.org/wiki/Coat_of_arms

Another commonly seen charge is the eagle, which is a symbol attributed to Saladin, and the hawk of the Qureish. They are commonly found as supporters in the heraldic achievements of several nations in the Near and Middle Eastern region.

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Note added at 1 hr (2010-05-19 16:21:03 GMT)
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AND from a glossary of Heraldic Terms:

The supporters, however, to the arms of the Earl of HUNTINGDON are without horns. The Triton, or mer-man, occurs as a supporter, e.g. to the arms of Lord LYTTELTON, and in more than one instance as a crest, e.g. of Sir Tatton SYKES and of the family of LANG in Leicestershire and Suffolk. The Neptune, q.v., in the arms of Sir Isaac HEARD, Garter King of Arms 1750, is sometimes blazoned as a Triton. The supporters to the Insignia of 'The ACADEMY OF THE MUSES,' London, were 'dexter, a Satyr; sinister, a Mer-man.'

http://www.4crests.com/sheraldicterms.html