Equinox vs. Solstice

You could almost think of them as opposites. The word "solstice" comes from the Latin roots "sol," meaning sun, and "sistere," meaning "stationary." That refers to the fact that during a solstice, the sun rises and appears to stop in the middle of the sky for a while before it sets. As a result, the summer solstice is the longest day of the year.
If you are on the opposite side of the globe from that sunny standstill, you would experience a winter solstice, the longest night of the year. The winter solstice occurs on December 21 or 22 in the Northern Hemisphere and on June 20 or 21 in the Southern Hemisphere. The summer solstice occurs on June 20 or 21 in the Northern Hemisphere and on December 21 or 22 in the Southern Hemisphere.
The word "equinox," comes from the Latin roots "aequus," meaning equal, and "nox," meaning night. On the equinox, day and night last for exactly the same amount of time. Spring equinox means spring has arrived. The vernal equinox happens about March 21 in the Northern Hemisphere and September 23 in the Southern Hemisphere. The autumnal equinox occurs near September 23 in the Northern Hemisphere and March 21 in the Southern Hemisphere.
Picture the Earth as it circles the sun. Our planet does not sit directly upright as it rotates; its axis of rotation is actually tilted by about 23.4 degrees, always pointed in the same direction in space. In the same way you get more sun on your shoulders if you are sitting up in your beach chair than you will if you are lounging flat, some areas of the Earth get more sunlight depending on where its axis is pointing. That, in turn, depends on where the planet is in its revolution around the sun.
For example, when it's the winter solstice in the Northern Hemisphere, the Earth is at a point in its revolution where its axis points away from the sun and the Northern Hemisphere gets the least amount of sunlight. If you were standing at the North Pole, you wouldn't get any sunlight at all. The Southern Hemisphere, on the other hand, would get its biggest helping of sunlight all year, making it the summer solstice there. In Antarctica, the sun never sets during this period.

Whereas the Earth's axis is tilted directly toward or away from the sun during a solstice, it's tilted directly askew from the sun during an equinox. To use the sunbathing example again, it's as if you rotated your body parallel to the towel clockwise you get the same amount of sun on your front and back as if you had rotated the other way. At this time, the sun is directly above the equator, and that means that day and night are of equal length. But not for long: A new season is upon you, which means shorter nights (or days!) and more (or less!) sunlight to enjoy.