An archaic verb meaning 'to go around' or 'to tour/visit' (old reading 'みる').
殿は国中を廻る（みる）巡察に出立した。
The lord set out on an inspection tour around the country.
昔の旅人は街道を廻る（みる）途中で宿に泊まった。
Old travelers, while going around the road, stayed overnight at inns.