A brief Internet search reveals the definition as "thin strips of meat or flesh," but then I also found this, and this, which I really hope are not considered meat or fish.
Edit: aiguillettes are the corded loops on some military uniforms. Who knew? (Not I.) Usage:
"The most obvious difference, however, was that officers wore their gold aiguillettes on the right shoulder, and thus buttoned the kurtka across from left to right." (Ronald Pawly, Patrice Courcelle, Napoleon's Red Lancers, Osprey, 2003, p. 11)
"'If a duck lack unction, it forfeits all rights to the name,' said Stephen. 'Yet here are some aiguillettes—what is the English for aiguillettes?—from the creature's inner flank that will go down well enough...'" —P. O'Brian, The Commodore, 160