A photometric system is a set of defined passbands for filters of known sensitivity to various wavelengths of electromagnetic radiation (EMR). The term is generally used regarding EMR in the infrared-to-ultraviolet range. With the specification of passbands, color indices have precise meanings.
An early system gaining common use was the Johnson-Morgan UBV photometric system, which is generally still assumed if no system is specified or implied. Equipment and scientific needs have prompted the development of new systems, and a major mission or survey (e.g., the Sloan Digital Sky Survey) often specifies its own. Conversion of photometric data from one system to another is non-trivial, given the differences in sensitivity functions, and cannot be exact: is an approximation at best, but for data specific to stars, the patterns in stellar spectral energy distributions allow for better approximations.
The passbands/filters are generally indicated by letter, some being mnemonic for the color, e.g., B for blue, R for red, but the same letter may have differing specifications under different systems.