According to George R. R. Martin, this is caused by magic.
The uber-Seasons of Westeros are most likely not seasons at all, but an unnatural Ice Age that covers the world. Thus "Winter" is the presence of this Ice Age, and "Summer" is the lack of Winter, or what we think of as normal seasons. Snow does fall during Summer, and the term "summer snows" from one of Martin's short stories is said to be the inspiration for this cycle.
As hinted in the series title,, two major unspoken sources of magic are at war with each other. Ice manifests itself as the White Walkers, the great forgotten enemy in the Land of Always Winter, north of John Snow's Wall. Fire manifests itself in Daenerys' dragons, and possibly Daenerys herself. Clearly these two forces are the "big heavies" of the series.
Thus when Ice rises in power, Winter descends on the world, until Fire rises to strike Ice back down. The characters of the series are mostly oblivious to the existence of magic and the causes of this cycle.
Still, we don't know how magic causes this Winter. Perhaps magic creates a scientific unbalancing of the planet's axis? There are a number of deep flaws to this theory, or weird Milankovitch cycles, or elongated orbits.
An unbalanced planetary axis (caused by a Milankovitch cycle or otherwise) would create a long Winter in one hemisphere and a long Summer in the other. There would be months of darkness during Winter and endless daytime during Summer. Summer would be as brutal as Winter, and there would also be elongated spring and fall. However, the characters talk about none of this, only of a brutal Winter that covers the world.
There are other consequences to an extreme planetary axis, as you can read in
What about elongated orbits? This would be measurable and predictable, and Westeros' Winter is not predictable. Consider that the Maesters recognize the difference between years and seasons. Years occur as we would expect. Lives are measured in years, and the world's history is recorded in years. Years are likely measured from astronomy just like the real world. Yet Winter is the great unknown in Westeros. It cannot be planned for. Plus the characters do not speak of the weak light that would occur from a protracted orbit.
This website goes into all kinds of practical consequences of this cycle:
In the end, I suspect that Ice magic has a great source in the lands north of the Wall, and every once in a while that source kicks up and generates a lot of magical cold. Kind of like a magical reverse space heater. Then Fire rises to shut off that source.More questions on Game of Thrones (TV series):