“Winter is Coming” is the motto of House Stark. The meaning behind these words is one of warning and constant vigilance. The Starks, being the lords of the North, strive to always be prepared for the coming of winter, which hits their lands the hardest.
A deeper, metaphorical sense can also be found in the motto. According to George R.R. Martin, it more generally expresses the sentiment that there are always dark periods in each of our lives, and even if things are good now (“summer”), we must always be ready for a dark period when events turn against us (“winter”).
In layman’s terms, it means that bad things are coming, no matter how good they may seem, and you should be prepared.