The vernal (spring) equinox occurred on March 20th this year for the northern hemisphere. While this marks the 1st day of spring for the northern hemisphere, this is the start of the fall season for the southern hemisphere.
So you may be asking yourself, what is actually happening on this day? What is happening is that the sun appears to cross the equator (the line that divides the northern hemisphere from the southern hemisphere) on this day, as part of its northward journey towards the Tropic of Cancer. Technically, the sun is not moving farther north, rather the Earth is shifting underneath the sun, and the sun in turn appears to be moving farther north in the sky. The earth rotates on a tilted axis (23.5 degrees) as it rotates around the sun along an imaginary line we call the ecliptic. All of the planets travel along this imaginary plane around the sun year after year. The below image may help you to understand what is happening.
It is the tilted axis of the Earth's spin that gives us our seasons. You may have noticed in the above image that the northern hemisphere is tilted towards the sun while the southern hemisphere is facing away from the sun during the June solstice. While we know this to be the first day of summer in the northern hemisphere, this would make the June solstice the first day of winter for the southern hemisphere. The opposite is true on the January solstice.
To recap, during the March equinox, the sun is directly over the equator and will continue to move farther and farther north in our sky until the summer solstice, during which time the sun will appear to start moving back south (lower in the sky), causing the days to get shorter and the nights longer. In the meantime, enjoy the longer days and the warmer temperatures that tend to come with the extra sunlight.