To walk through or over; especially, to travel over for the purpose of surveying or examining; to inspect by traversing; specifically, to inspect officially the boundaries of, as of a town or parish, by walking over the whole line.

To walk about; to ramble; to stroll; as, he perambulated in the park.

make an official inspection on foot of (the bounds of a property); "Selectmen are required by law to perambulate the bounds every five years"

Although often used as a synonym for "saunter," to perambulate is simply to ambulate in a circle. What's the point of that? See: AMBULATE.