According to Greek mythology, Apollo was the god of light who resided in the sun. He was the healer, the purifier, the bane of evil; since light and heat are not always beneficial, he was also the sender of pestilence and destruction. Sunlight without water will burn up crops and bring pestilence. The thought of "destruction" is taken from this latter phase of Apollo's nature.
Meta. Examination or investigation into Truth. Truth passes through several stages in entering the mind: first doubt, then examination, then a great desire for the Truth, then acceptance. These are represented by the Gentile cities--Amphipolis, Apollonia, and Thessalonica--through which Paul passed, and Beroea where "they received the word with all readiness of mind." The critical, investigating state of mind represented by Apollonia is of a destructive nature (destruction) while under carnal thought; but it is willing to examine into Truth, and as it becomes more and more guided by wisdom and love it becomes a great help in the spiritual life of the individual.