It just means an excursion or a going out based on the French verb, 'sortir', meaning to go out. In the same way, when forces people refer to a battle, they are using the French word, 'bataille'. That was the most direct source of the word in English.
From a technical point of view each individual aircraft takeoff from its home base counts as a sortie, so when in a report an Air Force spokesperson says "we flew 120 sorties over two days" that could be 120 aircraft making one trip each, or 60 aircraft making 2 trips etc all the way down to one extremely busy pilot!