Why? To produce an international standard while maintaining the two most common speed rating methods.
To fill in some details:
There were two common film speed standards in the west: ASA and DIN. The ISO technical committee responsible for film speeds (which happens to be lead by ANSI, the successor to the ASA) combined them, continuing both. Nowadays you can use either an ISO speed that is the same as ASA film speed, or an ISO speed that is the equivalent of the DIN film speed. The former is arithmetic (double the speed, double the number) and the latter is logarithmic (double the speed and add three to the number). The logarithmic version is distinguished by being followed by the degree symbol, eg 21° although the number values themselves usually tell you which version is being used.
The manufacturers have a lot more wiggle room with the ISO for digital cameras than they do with film. They are all stated to a fixed set of numbers that are a third of a stop apart, so there is no such thing as ISO 110, for example.
Apart from digital, there are standards for B&W silver-image negative film, colour negative film, and colour reversal film, all for still camera use. All other types of film, including motion picture film, cannot really quote an ISO speed - they have to use an EI (Exposure Index) which is a manufacturer's recommendation rather than a standardized speed. Numerically it equals ISO.