What unit of measurement does a wind vane measure?

It shows the direction where the wind is coming from. Like the North, South, East or west.

Weather vane or wind vane does not measure anything, it just shows the direction the wind is out of, a wind monitor measures the force the wind is blowing, in mph or kph.

Wind vanes indicate wind direction and when this information is recorded, describes the direction FROM which the wind is blowing.

Wind vanes measure the direction in which the wind is blowing.

anemometer

The direction the wind is blowing from.

So it measures wind direction.