1540s, from Latin augur, a religious official in ancient Rome who foretold events by observing and interpreting signs and omens, perhaps originally meaning "an increase in crops enacted in ritual," in which case it probably is from Old Latin *augos (genitive *augeris) "increase," and is related to augere "increase," from PIE root *aug- (1) "to increase."
The more popular theory is that it is from Latin avis "bird," because the flights, singing, and feeding of birds were important objects of divination (compare auspex). In that case, the second element would be from garrire "to talk." Related: Augural; augurial.
These auspices were studied, with a fixed ceremonial, in the following classes of phenomena: (1) signs from the heavens, including thunder and lightning, and other meteorological manifestations; (2) signs from the direction of flight or the various cries of birds; (3) signs from the manner of eating of domestic hens kept for this purpose; (4) signs from the movements and attitudes of animals; (5) evil omens from various fortuitous incidents, such as the fall of any object, the gnawing of a mouse, the creaking of a chair, etc., occurring during the augural ceremonies or when these were about to begin. [Century Dictionary]