If the Moon's orbit about the Earth was in exactly the same plane as the Earth's orbit about the Sun, we would see a solar eclipse once a month at every new moon, and we would see a lunar eclipse once a month at every full moon.
The Moon's orbit is instead inclined with respect to the Earth's orbit about the Sun, which means we only see a solar eclipse when the Moon's orbit crosses the ecliptic exactly at the time of the New Moon. This can happen when the Moon is at an ascending node, which is the case for the 8 April 2024 solar eclipse, or when the Moon is at a descending node, which was the case for the 21 August 2017 solar eclipse.
If a solar eclipse occurs when the Moon is at an ascending node, the north-south portion of the path of the eclipse will generally be south to north, following the ascending path of the Moon's motion. The path will generally be north to south when a solar eclipse occurs when the Moon is at a descending node.
The west to east motion is because the Moon orbits the Earth from west to east. The Moon's orbit velocity is over 1 km per second. The Earth's rotation results in an east to west rotation of less than half this value, and then only at the equator. The west to east motion of the Moon generally predominates over the Earth's rotation.
There are exceptions to the above. Despite occurring at a descending node, the initial path of the 21 August 2017 solar eclipse had a slight northward bend to its path before turning toward the southeast. Despite occurring at an ascending node, the final path of the 8 April 2024 solar eclipse will have a slight southward bend to its path, after having traveled northeast during most of the path. The path of the 23 November 2003 solar eclipse, which occurred mostly over Antarctica, was rather bizarre. It's path started moving mostly to the south, then turned toward the east, then toward the north. At the very end of the eclipse the path had a slight westward component.
The reason for these exceptions is that the Earth's rotation axis is tilted with respect to the ecliptic by about 23 degrees. Despite these exceptions, the general rule is that
- The path of solar eclipses move from west to east due to the Moon's orbital motion.
- The path of ascending node solar eclipses move from south to north, again due to the Moon's orbital motion.
- The path of descending node solar eclipses move from north to south, yet again due to the Moon's orbital motion.
- The paths of solar eclipses that occur at high latitudes are generally bizarre.