Fahrenheit is the name of the temperature scale used in the United States of America for ordinary purposes. It was used in most English-speaking countries until the 1960s. Most other countries use Celsius (which was known as Centigrade until 1960), which is part of the International System of Units (the "metric system").
The Fahrenheit temperature scale was invented by Daniel Gabriel Fahrenheit in 1724. He decided that the zero point should be the temperature of a mix of ammonium chloride and ice, because this was the very coldest temperature he could achieve in his laboratory. He decided to set 100 at the temperature of the human body. (Either he made his measurement inaccurately, or he was running a very slight fever at the time). On this scale, it turns out that water freezes at 32 degrees and boils at 212 degrees Fahrenheit.
To convert a temperature expressed in Celsius to Fahrenheit, multiply by 9/5 and add 32.
To convert a temperature in Fahrenheit to Celsius, subtract 32 and multiply the result by 5/9.
The temperature -40 is the same in both scales. This gives an alternative conversion rule: to convert in either direction, first add 40; then multiply by 5/9 for °F->°C or 9/5 for °C->°F; then subtract 40.