The Freeze was a human-engineered catastrophic event that occurred seven years ago during the boarding of Snowpiercer.
It was an attempt to reverse the effects of global warming using CW-7, however it went disastrously wrong and instead caused a massive drop in temperatures which froze the Earth so severely that no life could survive; Snowpiercer and Big Alice carry the only known survivors of humanity.[1]
It is revealed that the temperature outside the train during its passing of Yukon, Canada is around -120 degrees Celsius.
In Season 2, Melanie discovers snow falling despite the fact that it is supposedly too cold for snow, suggesting that the planet is begining to recover from the Freeze.