From 恭喜 ("to congratulate, respectfully wishing one joy") + 發財 ("to become rich, to make money"). Literally, "congratulations for becoming rich". Originated in post-Opium War Guangzhou Cantonese, now a general Chinese phrase.
Ma Jiahui, "Us - Some Happiness and Sadness about This Era": "He liked to call a restaurant on every New Year's Day (of the lunar calendar), as he knew clearly the lady there answering the phone would inevitably greet him with 'Kung Hei Fat Choi'. Upon hearing this he (Zhou Shi) would promptly reply by saying 'Thank you, thank you' and then just hang up. His reason for doing this was just to get an auspicious start of the new year, not an act of patronisation."