They are the words for House Stark. Most of the major houses have some words that are supposed to represent them and their reputation in some way.
As reflected on by Catelyn;
"Yes," Catelyn agreed. The words gave her a chill, as they always did. The Stark words. Every noble house had its words. Family mottoes, touchstones, prayers of sorts, they boasted of honor and glory, promised loyalty and truth, swore faith and courage. All but the Starks. Winter is coming, said the Stark words. Not for the first time, she reflected on what a strange people these northerners were.
A Game of Thrones - Catelyn I
We see that House Words are important things to learn for young lordlings;
And Olenna Tyrell (if you are only on season 1, be wary of spoilers) mocks her own house words and says the Stark's are memorable;
The words themselves are quite literal, a reminder that winters in this world can last for years;
She perched anxiously on the edge of her bed. "You are too young to be burdened with all my cares," he told her, "but you are also a Stark of Winterfell. You know our words."
"Winter is coming," Arya whispered.
"The hard cruel times," her father said. "We tasted them on the Trident, child, and when Bran fell. You were born in the long summer, sweet one, you've never known anything else, but now the winter is truly coming. Remember the sigil of our House, Arya."
A Game of Thrones - Arya II
It is a stark (get it, nudge nudge) reminder that if you are not prepared you will surely die;
"Because it will not last," Catelyn answered, sadly. "Because they are the knights of summer, and winter is coming."
"Lady Catelyn, you are wrong." Brienne regarded her with eyes as blue as her armor. "Winter will never come for the likes of us. Should we die in battle, they will surely sing of us, and it's always summer in the songs. In the songs all knights are gallant, all maids are beautiful, and the sun is always shining."
A Clash of Kings - Catelyn II