GSM 850 is simply GSM technology operating in the Cellular (850 MHz or "800") frequency band. Both the technology and frequency band have been around for many years, but not until 2002 were they combined.
In the U.S. prior to 2002, GSM technology only operated in the PCS (1900 MHz) frequency band.
Cellular (850) and PCS (1900) are the two primary bands used for cell phones in the U.S. and much of the Americas.
GSM 850 was created for carriers with Cellular (850) licenses when they switched from other, older technologies to GSM.
Before the existence of GSM 850, the Cellular band was commonly referred to as the "800 MHz" band. "850 MHz" implies a different frequency band, but this is not the case. "800 MHz" and "850 MHz" refer to the exact same frequency band. 850 is technically a more accurate description of the frequency range, although "800" is still common when referring to CDMA and AMPS (analog) technology.
Despite the close number, GSM 850 is not compatible with GSM 900 used in Europe and Asia. A phone that only has GSM 850 cannot work on a GSM 900 network, nor vice-versa.