The Genève line was introduced in 1952 (some say '53), and, with the exception of the very low production Chronometres, sat at the top of OMEGA's model line of hand-wind watches throughout the 1950s. The cases featured elegantly chamfered lugs, and the indexes were made of gold. The 30mm movements, while no different from those used in other models of the period, had achieved notable success in the Geneva Observatory Trials (along with Neuchâtel, and others). In 1945 an early version won first prize, which was followed by other awards and records set during the 1950s. So, Omega chose to use Genève as a reference to those successes, and obviously applied to name to a high-end model.
They are, to my mind, a quintessentially understated yet elegant model, reflecting both the quality of Omega and ethos of the period very well.