Winter in the world of A Song of Ice and Fire works very differently than a real-world winter.

The "seasons" are broken up into a binary system, Summer and Winter. It is implied that in the times of Winter snow creeps up as high as castle walls and the cold is unbearable. These Winters can last decades sort of like an Ice Age.

These words are the motto of House Stark, presumably because of their close proximity to the Wall and the Lands of Always Winter.

Currently, the shows events are taking place during a ~10yr Summer that started shortly before Brandon was born.

In the land of Westeros seasons can last many years.

The phrase, "Winter is Coming", is a constant reminder that there will be a time when you will not be able to grow food, people will die of both frost and famine, and, above all, time is fleeting. It is the motto of the Stark Clan.

Another common phrase, at least in the books and in the first season, is "These are the acts of green summer men". Which, in my opinion, means the care-free nature that comes with a time of plenty has not yet needed to be shed. When you live in plenty you don't always think of the times of less. The Stark words seem to be "remember that there will be a time that we will need to band together for our own survival".

This significance is also increased with the threat of the White Walkers and the Others coming to attack. begin speculation These beings are basically the embodiment of death and the other spoken of by the Red Woman.

From what I've gathered of what I've seen of the first season so far, their world has a "summer" and "winter" periods. The summer being long periods of good light and warmer weather and the winder being long period of no light and colder weather.

It's implied that the current "summer" has lasted about nine years, maybe more. It's hinted that the next winter will be a long, cold, and dark winter and that it'll bring a lot of bad things with it.

Alternatively 'winter' could refer to the 'horrors' (i.e. White Walkers) that reside beyond the wall.

Therefore, when they say 'winter is coming' they could not only refer to the season and the resulting drop in temperature but they could also be refering to what will be 'invading' when/if the nights watch fail and the wall is breached.

Winter is a season that can last for years, possibly even decades.

This is true for summers as well, but the seasons are not binary, Spring and Fall exist as well.

This is backed up by many other characters point of views.

Old Nan tells us in "Lord Snow" (S01E03);

"Oh, my sweet summer child. What do you know about fear? Fear is for the winter, when the snows fall a hundred feet deep. Fear is for the long night, when the sun hides for years and children are born and live and die all in darkness.

Tyrion reflects on the seasons in his life;

"As you say, my lord." He had been born in the dead of winter, a terrible cruel one that the maesters said had lasted near three years, but Tyrion's earliest memories were of spring.

"When I was a boy, it was said that a long summer always meant a long winter to come. This summer has lasted nine years, Tyrion, and a tenth will soon be upon us. Think on that."

_{A Game of Thrones - Tyrion III}

Grand Maester Pycelle rambles some history;

There were fools, even in the Citadel, who took that to mean that the Great Summer had come at last, the summer that never ends, but in the seventh year it broke suddenly, and we had a short autumn and a terrible long winter.

_{A Game of Thrones - Eddard V}

There is even a time called the Year of the False Spring which expanded in the books but made its way into the show in the Histories & Lore: House Reed

When he was a young man in the Year of the False Spring, a great southern lord held the largest tourney Westeros had ever seen in the largest castle Westeros had ever seen.

In this series their seasons take years long not as normal to us so they mean that years of winter are coming and they are afraid of the horrible things that happen during it and especially the white walkers when happened exactly.