Mid-December marks the southern solstice. During southern solstice, the tropic of Capricorn receives sunlight from directly overhead. If you stood along the Tropic of Capricorn at noon during solstice, you would effectively have no shadow - it would be completely underneath your feet. This is commonly called winter solstice in northern countries. Mid-June marks the northern solstice, where the same thing happens for the Tropic of Cancer.
Wobble
Solstice occurs for all planets. There is a variation in the length of days and the position of the Sun in the sky because planets wobble along their orbits. Most planets rotate perpendicular to the path of their orbit with poles pointing more or less perpendicular to the orbital plane. Uranus is notable; it has an axial tilt of 98 degrees. Uranus wobbles so extremely that during it's solstice a pole points to the Sun, and during equinox its equator faces the Sun.
Orbit
Planets orbit stars because they are trapped in a very large four-dimensional funnel, with the star in the middle. The heavy masses of stars depress space-time with gravity, creating a curve where other bodies loop around. If a planet or other body has too much speed it will fling itself away from the star. If the body has too little speed it will spiral into the star. Thankfully, the Earth has just the right amount of speed to stay in orbit around the Sun. There is evidence from observation of other star systems that planets frequently spiral towards their stars, so we are pretty lucky.
Angular Momentum
Planets form around stars shortly after stars are born in a nebula or other dense cloud of dust and gas. This material condenses and forms the star and a small amount that didn't make it into the star forms a lumpy accretion disc. Gravity pulls small clumps of material together into larger clumps and planets eventually form.
The star, accretion disc, and later the planets all rotate in the same direction. At the atomic scale, as the star forms, each atom has a tiny amount of spin due to angular momentum (this is a quantum property). The spin of the atoms are pretty random at the beginning, but there is a small net spin in one direction over the entire system. As the dust cloud condenses this net spin gets "amplified", just as a spinning figure skater spins faster when he holds his arms in. There is still some variation in different areas of the system leading to wobble and other chaotic artifacts that make a star system unique.
