What are equinox and solstices dates? What happens to light and dark during these times? Where is it dark or light?

Equinoxes and solstices happen due to the tilt of the Earth on its axis.  Solstices occur when the Earth is at a maximum angle away from the Sun.  During the summer solstice the sun is directly over the Tropic of Cancer.  North of this latitude line locations experience the longest day of the year (meaning they get the most sunlight on that day).  The summer solstice typically occurs around June 21st.  Around December 21st, we experience the winter solstice.  The winter solstice occurs when the sun is directly over the Tropic of Capricorn.  The winter solstice represents the day with the least amount of sunlight in the Northern Hemisphere. 
Equinoxes, on the other hand, represent the point when the Earth’s axis is relatively straight in comparison to the sun.  During these days, the sun shines directly on the equator, causing an almost equal amount of daylight and night time.  The vernal equinox occurs on approximately March 20th and the autumnal equinox happens around September 22nd. 
Please refer to the National Weather Service website link below, which provides a visual explanation of this concept.