The metre was originally defined in 1791 by the French Academy of Sciences as 1/10,000,000 of the distance along the Earth's surface from the North Pole to the Equator along the meridian of Paris. Uncertainty in the measurement of that distance lead the International Bureau of Weights and Measures in 1889 to redefine the metre as the distance between two lines on a standard bar of platinum-iridium kept at Sevres.
In 1960, as lasers had become available, the 11th General Conference on Weights and Measures changed the definition of metre to be the length of 1,650,763.73 wavelengths in vacuum of the orange-red emission line in the spectrum of krypton-86. In 1983 the General Conference on Weights and Measures defined the metre as the distance traveled by light in a vacuum in 1/299,792,458 of a second (that is, the speed of light in a vacuum was defined to be 299,792,458 metres per second). Since the speed of light is believed to be constant everywhere, a definition based on light is easier to maintain and more consistent than a measurement based on the circumference of the Earth or the length of a specific metal bar. Thus, should the bar be destroyed or lost, the standard meter can still be easily recreated in any laboratory.
Metre refers to the measurement of a musical line into units such as beats and measures, indicated in Western notation by a symbol called a time signature. Properly, "metre" describes the whole concept of measuring rhythmic units, but it can also be used as a specific descriptor for a measurement of an individual piece as represented by the time signature -- e.g., "This piece is in 4/4 metre" is equivalent to "This piece is in 4/4 time" or "This piece has a 4/4 time signature."