Wikipedia
A Nabedrennik ( Church Slavonic: набедренникъ, "On the thigh") is a vestment worn by some Russian Orthodox priests. It is a square or rectangular cloth worn at the right hip, suspended from a strap attached to the two upper corners of the vestment and drawn over the left shoulder. Unlike all other priestly vestments, the nabedrennik has no associated vesting prayer.
A relatively recent Russian usage, the nabedrennik is worn only in the Russian tradition by a presbyter to whom it has been awarded by his bishop; it is not worn by bishops. It is never worn in the Greek tradition. The award is given "for long and dedicated service" to the Church.
The rectangular shape of the nabedrennik differs from the epigonation, which is lozenge shaped. Both are believed to derive from the ancient knee guards which shielded the legs of warriors from being bruised by their swords. The Byzantine Emperors used to award swords to their commanders and nobles; in the same way the Church awards priests who defend the faith. If the epigonation (Church Slavonic: палица, palitsa, "club") is also awarded to the same priest, he wears both but shifts the nabedrennik to the left side.