Metric units of length are used to measure the distance between two points or the length of an object. The metric system is a decimal-based system of measurement that is widely used around the world. It is based on multiples of ten, which makes conversions between different units easy.

The metric unit of length is the meter (m).

Explanation:
1. Inch: An inch is not a metric unit of length. It is a customary unit of length used in the United States, Canada, and the United Kingdom. 1 inch is equal to 2.54 centimeters.
2. Yard: A yard is also not a metric unit of length. It is a customary unit of length used in the United States and the United Kingdom. 1 yard is equal to 0.9144 meters.
3. Meter: The meter is the basic unit of length in the metric system. It is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second. The meter is used in most countries around the world for scientific, industrial, and everyday measurements.
4. Mile: The mile is not a metric unit of length. It is a customary unit of length used primarily in the United States and the United Kingdom. 1 mile is equal to 1.60934 kilometers.

In summary, the metric unit of length is the meter (m). It is the basic unit of length in the metric system and is used in most countries around the world. The other options mentioned in the question (inch, yard, mile) are not metric units of length.