The vernal and autumnal equinoxes are the two times each year when the Sun and the Earth's equator are on the same plane. On this day sunset and sunrise are almost exactly 12 hours apart. The vernal equinox is usually around March 20 and the autumnal equinox is about September 23. The exact dates vary because a year is really 365 1/4 days long, a fact that we have to adjust for by using leap years.
The reason that day and night are equal in length on the equinox is because the earth's axis is perpendicular to its orbit, so the terminator, which is the shadow line on earth separating night from day, runs from pole to pole. This means that no matter what latitude you are at, it takes the same amount of time to go from one terminator to the next as the earth rotates.