in perfect order; without a hitch; flawlessly
Describes a performance, formation, or coordinated action that is executed with flawless precision, as if not a single thread is out of place. Often used for military drills, dance, or group movements.
The athletes marched in perfect order.
The dancers' movements were flawless and captivated the audience.
From 一糸 (one thread) + 乱れず (not disordered). The image is that not even a single thread is out of place, indicating perfect order.