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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 wide 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 sometimes develops its own, e.g., the ugriz photometric system for the Sloan Digital Sky Survey. Among the other systems:
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.
Conversion of photometric data from one system to another is non-trivial, given the differences in sensitivity functions, and is inherently inconsistent, being an approximation at best. Specifically for stars, which are primarily black-body and follow other general patterns, there are conversion formulae that produce reasonable approximations.
To cite filtered photometric data as magnitudes, a zero-point must be adopted for each passband (calibration). A traditional calibration system is termed the Vega system, designed to make the star, Vega zero for each passband. A newer alternative, the AB system, simply uses a fixed spectral flux density (3631 janskys) as zero for each passband. The Vega system was traditionally used with the UBV photometric system, but for recent citations, it is worth checking which is being used if you are depending upon the value.