counter for tours, cycles, rounds, circuits
Used after a number to count complete cycles, rounds, or circuits of an activity or journey. Often seen in contexts like patrols, tours, or repeated processes.
See also: 一巡
The security guard made one round of the building.
Three circuits of this course make exactly 10 kilometers.
周 is the everyday counter for laps around a track or course, while 巡 is a more literary word for rounds or cycles, as in patrol rounds.
The kanji 巡 means 'patrol' or 'go around', and the reading じゅん is the on'yomi. The counter usage derives naturally from the idea of making a round or circuit.