Sub-zero means below zero degrees — colder than the point where water freezes. It is an adjective and normally goes in front of a noun: sub-zero temperatures, sub-zero conditions, a sub-zero night. You would not usually say "the weather was sub-zero" on its own; "the temperature was below zero" is the natural way to say that.

It sounds slightly technical and dramatic, which is why weather reports, news stories, and product advertising like it. Coats, sleeping bags, and car batteries are sold as suitable for sub-zero conditions. Writers also stretch it away from weather to describe a person who is extremely cold in manner: sub-zero politeness, a sub-zero stare. That use is figurative and fairly rare, but you will meet it.

One thing worth knowing, and it matters for a student in Taiwan reading international news: which zero? In Celsius, zero is freezing point, so sub-zero and freezing mean roughly the same thing. In Fahrenheit, zero is about -18°C, so an American saying "sub-zero" is describing something far, far colder than a British writer usually means. Most writing outside the United States assumes Celsius, but if the number matters, check the scale. Note also that it is written with a hyphen most of the time, though subzero appears too, especially in American writing.