In the United States and the rest of the northern hemisphere, the first day of the spring season is the day of the year when the Sun crosses the celestial equator moving northward (on March 20th or 21st). This day is known as the Vernal Equinox.
A common misconception is that the earth is further from the sun in winter than in summer. Actually, the Earth is closest to the sun in December which is winter in the Northern hemisphere.