In geodesy, a meridian arc is the distance between two points with the same longitude. In geometry it is an arc: a segment of a curve. The length of an imaginary rope laid over the globe would be that distance.
Two or more such measurements at different places get the shape of the reference ellipsoid which is most like the shape of the geoid. This process is called "the determination of the figure of the Earth". The earliest determinations of the size of a spherical Earth used a single arc. The latest determinations use astro-geodetic measurements and the methods of satellite geodesy to get the reference ellipsoids.
The Alexandrian scientist Eratosthenes about 240 BC, first calculated a good value for circumference of the Earth. He knew that on the summer solstice at local noon the sun goes through the zenith in the ancient Egyptian city of Syene (Assuan). He also knew from his own measurements that, at the same moment in his hometown of Alexandria, the zenith distance was 1/50 of a full circle (7.2°). Assuming that Alexandria was due north of Syene, Eratosthenes concluded that the distance between Alexandria and Syene must be 1/50 of Earth's circumference.