Solstices and equinoxes
Days are long in summer and short in winter because the Earth's axis is tilted, not because the Earth is nearer the Sun. Four dates mark the extremes and the midpoints.
The tilt does the work
The Earth's axis of rotation is tilted about 23.44° with respect to the plane of its orbit, and it keeps pointing the same way as the planet goes round. For half the year the Northern Hemisphere leans towards the Sun: the Sun climbs higher, stays up longer, and days are long. For the other half it leans away: low Sun, short days. The Southern Hemisphere experiences the opposite at the same moment — a June heatwave in Delhi is midwinter in Sydney.
The solstices: longest and shortest days
A solstice is the moment the Sun reaches its most northerly or southerly path relative to the celestial equator. There are two each year, around 20–22 June and 20–22 December. At the June solstice the Sun is overhead at latitude 23.44°N, the Tropic of Cancer: it is the longest day in the Northern Hemisphere and the shortest in the Southern. At the December solstice the Sun is overhead at the Tropic of Capricorn, and the roles reverse. The exact date shifts by a day or so from year to year because the calendar year is not exactly the orbital year — the same mismatch that leap years correct.
The equinoxes: equal day and night
Halfway between the solstices, around 20 March and 22–23 September, the Sun is overhead at the equator and day and night are close to equal everywhere on Earth. From the March equinox the north gains daylight day by day until June; from September it loses it until December.
How much it varies depends on where you are
At the equator day length barely changes all year; the swing between the longest and shortest day grows with latitude, and beyond the polar circles the extremes become months of continuous daylight or darkness.
Why the year does not start on a solstice
It would be tidy if 1 January were the December solstice, and it very nearly is: the two are about ten days apart. That gap is history, not astronomy. The Romans fixed 1 January as the start of the year for civic reasons, and the Julian and Gregorian calendars kept the date — the full story is in why New Year is on 1 January. The countdown counts to that civic midnight, in your time zone, not to any point in the orbit.
Sources
- Solstice — Wikipedia (definition, dates, 23.44°, tropics, equinox dates)