Caption: The solstices and the solstice seasons (i.e., summer and winter) from the ecliptic plane perspective. Not-to-scale.

When the Sun is above the celestial equator (an invisible line perpendicular to the celestial axis that runs through the Earth), it beams more directly down on the Northern Hemisphere of the Earth and stays above the horizon longer in the Northern Hemisphere. In fact to some latitude south from the North Pole, the Sun never sets as is clear diagrammatically.

When the Sun is below the celestial equator, it beams less directly on Northern Hemisphere of the Earth and stays above the horizon for less time in the Northern Hemisphere. In fact to some latitude south from the North Pole, the Sun never rises as is clear diagrammatically.

The Southern Hemisphere requires same discussion mutatis mutandis.

When the Sun beams most/least directly on a hemisphere that hemisphere has summer/winter.

Note that the direction of the Earth's axis relative to the observable universe is approximately fixed over relatively short time scales. However, there is actually an axial precession about the ecliptic pole with a period of ∼ 26,000 Julian years (Jyr) (see Wikipedia: Axial precession). The axial precession is caused by the combination of the Earth's rotation and the torque on the Earth caused by (in order of importance) the Moon, the Sun, and the planets.

For more on the axial precession, see figures axial_precession_animation.html axial_precession_physics, and axial_precession_year.html.

Credit/Permission: © David Jeffery, 2003 / Own work.
Image link: Itself.
Local file: local link: season_solstices.html.
File: Earth file: season_solstices.html.