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"Aurora" in Latin means "dawn", as opposed to "sunrise" (which is "ortus solis", the rising of the sun). This would mean, more or less, the period at which the sky was visibly bright.
The reason for selecting this time was undoubtedly so that Mass would not fall before celebration of Lauds, that part of the Divine Office which was intended to open the day. According to the Catholic Encyclopedia, "The office of Lauds was supposed to be recited at dawn." It seems likely that this general directive could be interpreted differently by various priests, and surely some priests celebrated Lauds quite early in the morning. Hence the directive in the 1917 Code made sure that no matter how early Lauds was celebrated, Mass would come after it. (In convents or monasteries which celebrate the Divine Office, the first Mass of the day is often celebrated immediately after, or at least very shortly after, the end of Lauds.