The Earth is an oblate spheroid. It is slightly flattened at the poles, and bulges at the Equator. Thus, the curvature is not perfectly uniform. The actual physical length of “one minute of arc of latitude” is approximately 1843 metres at the Equator and 1861 metres at the Poles. To ensure a consistent standard, the Nautical Mile was set as the average value, exactly 1852 metres.

“of one minute of arc of latitude measured along a meridian of longitude.” → CORRECT. Meridians are lines that run from South pole to North pole and are great circles (are circumferences of the Earth). Measuring latitude along a meridian gives a nearly constant distance for every degree of arc. This allows to measure distance directly on a chart, using the latitude.

Therefore, a nautical mile is defined as the average length on the surface of the earth of of one minute of arc of latitude measured along a meridian of longitude. In contrast, meridians converge at the poles, so “one minute of longitude” becomes smaller the further you move from the Equator. So, it cannot be used as a standard for distance.

“of one minute of arc of latitude measured along the equator.” → INCORRECT. A nautical mile is defined as the average length on the surface of the earth of of one minute of arc of longitude measured along the Equator.

“of one minute of arc of longitude measured along a parallel of latitude.” → INCORRECT. While one minute of longitude at the equator is roughly equal to one nautical mile, this only occurs there. Because lines of longitude converge toward the poles, the distance of "one minute of longitude" decreases to zero at the poles.

“of one minute of arc of latitude measured along a small circle.” → INCORRECT. Parallels of latitude (except the equator) are considered "small circles". Thus, latitude itself is measured between these circles, not along them.