The most eloquent moment in a Byzantine ordination to the priesthood is a change of clothes. A deacon wears the orarion, a long narrow band, over the left shoulder with both ends hanging free. At his ordination as a priest the bishop takes the back end and brings it forward over the front of his body, so that the single band now hangs doubled down the front from the neck, and the people cry out Axios, he is worthy. The garment is not replaced; it is rearranged, and the rearrangement is the visible statement of what has changed.
The finished vestment is the epitrachelion, in practice made as one broad band with an opening for the head or as two bands joined down their length, marked with a row of crosses and usually finished with a fringe. The prayer said as it is put on is taken from the psalm about the precious ointment on the head of Aaron running down upon his beard and to the skirts of his garment, so the vesting formula points the wearer back to the Israelite priesthood rather than to any later office.
The name simply means upon the neck. It is worn over the sticharion and under the phelonion, and a bishop wears one too, under the sakkos, since the priesthood is not left behind on becoming a bishop.