Why do you see your breath on a cold day?

On a cold day, you can see your breath because the warm, moist air you exhale condenses into tiny droplets of liquid water. These droplets form because the air around you is colder than your breath, so the water vapor in your breath condenses into a liquid. The higher the difference between the temperature of your breath and the temperature of the air, the more visible your breath will be. That's why you can often see your breath more easily on a very cold day than on a mildly cold day.

The phenomenon of seeing your breath on a cold day is not unique to humans. Any warm-blooded animal will produce visible breath when the air is cold enough, including dogs, cats, horses, and even birds.