The adjective "auspicious" means favorable, fortunate, opportune or promising success. A common phrase is "an auspicious occasion," meaning an event that seems to be favored by fortune.
According to the Online Etymology Dictionary, the adjective "auspicious" comes from the Latin word "auspicium," meaning "of good omen." Usage of the word dates back to the 1590s and relates to the practice of divining the future by watching the flight of birds. The adverbial form is "auspiciously," and the noun form is "auspiciousness," though it is not commonly used. There is no verb form. However, adding the prefix "in-" gives the opposite of the word. "Inauspicious" means unfavorable or unlucky.