You might already know that when you breathe in you take in oxygen and when you breathe out you exhale carbon dioxide.
However, what you might not have realized before is that there's more in your breath than just the carbon dioxide, there is also moisture in your breath from your mouth and lungs.
When the moisture in your breath hits cold air, a little cloud or fog is formed.
Since the cold air around you cannot hold as much water as the warm air in your breath, the moisture in your breath condenses when it hits the cold air and forms into a little cloud.
It doesn't happen when the air around you is warm because the warm air can hold the moisture.
It's impossible to name the exact temperature at which you'll be able to see your breath, but a good estimate would be around 45 degrees Fahrenheit and below.