Today marks the beginning of meterological winter. There are really 3 different winters, depending on how you define winter (this is true for all four seasons).

Typically, we use the system of astronomical seasons. Astronomical winter begins in late December when the sun is directly above the tropic of Capricorn, otherwise known as the winter solstice. The sun begins moving north, and by the time the sun is directly over the equator in late March, winter comes to an end.

There is also the solar winter. This is the quarter of the year that has the least sunlight. The winter solstice  (the beginning of the astronomical winter), is exactly in the middle of the solar winter. The solar winter begins in late November and ends in early February.

Then we also have the meteorological winter. This is the quarter of the year that on average is the coldest and most "wintery". The meteorological winter is the entire month of December, January and February. This is just an average though, as early March can be colder than early December, but when you average the whole month December is colder.

There is also "temperature lag". Even though the northern hemisphere gets the least light in late December, mid-January is the coldest. Even though the days are beginning to get longer in January, it's not enough to warm things up and the climate continues to cool for several weeks after the winter solstice. There is still residual warmth from the summer (especially in the ocean), and it takes a long time for all that energy to radiate into space. Temperature lag also happens in the summer. Mid-July is the warmest, because it takes a while for the sun to warm up all the cold air and water left over from the winter.