seasons
Earth's axis is tilted 23.5 degrees. The axis is always tilted in the same direction. Because of this tilt, Sunlight shines differently on different areas of Earth, causing seasons. The number of daylight hours changes throughout the year as the Earth revolves around the Sun.
summer
When it is summer in the Northern Hemisphere, that part of Earth is tilted towards the Sun. This makes days longer and nights shorter. This also means that the Sun's rays strike the Earth at more direct angles, causing the temperature to be warmer. This would be opposite for the Southern Hemisphere, because they are tilted away from the Sun, it would be winter.
Winter
The Earth is actually closest to the Sun when it is winter in the Northern Hemisphere. However, the tilt is away from the Sun so the Northern Hemisphere receives less direct sunlight causing the temperature to be colder. This makes days shorter and nights longer. Again, this would be opposite for the Southern Hemisphere, so their summer is in January and their winter is in July.
Solstice
A solstice occurs in either the Summer (June 21) or Winter (December 21) when the Earth is either tilted the most toward the Sun, or the most away from the Sun. This signals the start of summer or the start of winter. During a Summer Solstice, the number of daylight hours is longest and nighttime hours is shortest (longest day of the year). During a Winter Solstice, the number of daylight hours is shortest and nighttime hours is longest (shortest day of the year)
equinox
"Equi" means equal, and "nox" means night. Therefore, equinox means "equal night", when the number of daylight hours and nighttime hours are the same. This occurs when the Earth is not tilted toward or away from the Sun. The Autumnal (Fall) Equinox occurs on September 21 and signals the start of Fall. The Vernal (Spring) Equinox occurs on March 21 and signals the start of Spring.