A film's speed refers to its sensitivity to light and is indicated by a value based on a standardized scale. The establishment of the current ISO (International Standards for Organization) film speed system is the result of several evolutions of sensitivity scales invented since photography's earliest days to measure and standardize the characteristics of a film's light-sensitive emulsion.
The first scale used a series of highly-pigmented squares which expressed sensitivity in degrees, known as the Warnerke system, named after Polish inventor Leon Warnerke. As new emulsions and light sources were developed, new systems of measuring emulsion sensitivity were created. Most involved mathematical formulas based on logarithmic scales derived from the minimum exposure required to produce a visible darkening of the emulsion when developed.
In the 1930s, Weston Electrical Instrument Corporation and General Electric introduced film rating systems, both of which applied to the photo-electric exposure meters they manufactured. These two systems led to the development of the ASA (American Standards Association, now ANSI) scale, which established both an arithmetic speed scale and logarithmic grades of film sensitivity representing the doubling of a film's speed with each full exposure stop.
Also established during this time was the DIN scale, a German logarithmic measurement of sensitometry, which used a base 10 logarithm multiplied by 10, and expressed in degrees. According to the DIN scale, a 3-degree (3°) increase doubles the film's light sensitivity.
In 1974, both the ASA and DIN systems were combined to form the current ISO standard, which defines scales for speeds of black and white (ISO 6), color negative (ISO 5800), and color reversal (slide) film (ISO 2240) using the arithmetic and logarithmic scale combination. The ASA's arithmetic scale corresponds to a doubling of film sensitivity by a doubling of the film speed number value (on the box and film canister). The logarithmic scale of the DIN system also indicates an emulsion's light sensitivity, is expressed in degrees, and often accompanies the ISO rating (and, has nothing to do with temperature). The two scales are expressed together as follows for a film with a speed rated at ISO 100: 100/21° (ASA/DIN)
Comparing films of different speeds, we can see how the scales work together and represent two historical methods of measuring the light-sensitivity of photographic emulsions: 50/18° versus 100/21° versus 200/24° versus 400/27° (the arithmetic value doubles as the logarithmic scale increases by a factor of 3 to indicate a film's speed).
If this concept seems overwhelming and cumbersome and difficult to absorb, think about it this way: just as we use measurement systems to quantify weight (ounces, pounds, grams), volume (pints, gallons, liters), distance and length (inches, miles, meters), temperature (celcius, Farenheit), and even time (seconds, minutes, hours), the film speed scale offers a standard way to express the light sensitivity of photographic emulsion so we can properly exposure our film for beautiful pictures.