Short answers, pulled from the story.
The metre is the base unit of length in the International System of Units, with the symbol m. Since 2019, it has been defined as the length of the path travelled by light in vacuum during a fixed time interval, where the second is set by a hyperfine transition frequency of caesium.
In 1791, the French National Assembly defined the metre as one ten-millionth of the distance from the equator to the North Pole, measured along a great circle through Paris. This set 10,000 metres as a quarter of the Earth's polar circumference.
The metre was redefined in 1799 using a prototype metre bar, with the bar itself changed in 1889. It was redefined again in 1960 using wavelengths of krypton-86, then in 1983 using light in vacuum, and slightly modified in 2002 and again in the 2019 revision of the SI.
Metre is the standard spelling of the metric unit of length in all English-speaking nations except the United States and the Philippines, which use meter. In English, meter is also used for measuring instruments, while poetry allows either metre or meter.
The word metre traces to the Greek verb metreo, meaning to measure, count or compare, and the noun metron, meaning a measure. The Greek word descends from the Proto-Indo-European root meh₁-, to measure, and the word entered English for the French unit mètre at least as early as 1797.
One metre is approximately 1.0936 yard and about 39.370 inches. A yard is exactly 0.9144 metre and an inch is exactly 0.0254 metre.