The meaning of the Game of Thrones (2011) phrase “Winter is coming” has a few layers. First, and most literally, it means exactly what it says -- winter is coming. The land of Westeros has very odd seasonal structures where summer and winter can last for long periods of time without anyone knowing when they will switch.
Second, it is the motto of House Stark, and refers to their vigilance. It is an expression that means one should always be prepared. As rulers of the North, they must always be ready for anything that could happen -- and eventually, something will. Thus, winter is coming.
Third, George R. R. Martin, creator of the book series on which the show is based, explains that there is also deeper metaphorical meaning generally expressing the sentiment that dark periods occur in life. Even if things are currently going well in your world ("summer"), this won't last forever. There will eventually come a dark period, a coldness, when events turn against us ("winter"). This metaphorical interpretation reflects the underlying message of the entire show, as nobody is ever safe or comfortable for too long.
The archetypal symbol of winter appears in other famous literary texts. For instance, in the opening line of Shakespeare's play Richard III, Richard of the House of York forewarns, "Now is the winter of our discontent/ Made glorious summer by this sun of York..." Parallel to the ominous warning behind the Game of Thrones' phrase, winter is used in the play as a metaphor to convey the dark and cold season wherein danger and even death may await.
Martin has also stated that the Hundred Years War is an inspiration for the Game of Thrones story. As History Behind Game of Thrones puts it, "All the problems of the fifteenth-century—the Great Famine, the low-crop yields, the populations who lived on the razor’s edge of starvation, whose weakened bodies were ripe pickings for the Black Death—were made worse by the war. But, it was the weather that caused many of these problems. Perhaps, appropriately, in Game of Thrones, the weather is the backdrop to everything."
For the Game of Thrones' characters, "winter is coming" undeniably suggests that doom, destruction and death will blow into their lives. Whether any given character survives the onslaught is not guaranteed.