As per TVTropes, of all places to get a good solid factual answer :)
The book tells us that this particular pillar is produced in response to one from Barad-dûr. The exchange is essentially Sauron (at Barad-dûr) asking "Are you ready?" and the Witch-King at Minas Morgul replying "Yes!"
Here's the relevant passage from "The Two Towers" that seems to confirm that this was either a "We are ready" or "We acknowledge the order to move out":
The great rumbling noise, louder than ever before, rolled in the ground and echoed in the mountains. Then with searing suddenness there came a great red flash. Far beyond the eastern mountains it leapt into the sky and splashed the lowering clouds with crimson. In that valley of shadow and cold deathly light it seemed unbearably violent and fierce.
And Minas Morgul answered. There was a flare of livid lightnings: forks of blue flame springing up from the tower and from the encircling hills into the sullen clouds.
Across the narrow valley, now almost on a level with his eyes, the walls of the evil city stood, and its cavernous gate, shaped like an open mouth with gleaming teeth, was gaping wide. And out of the gate an army came.
As a side note, for those who didn't notice this specific detail among the wall of quotes - while the movie scene was in the ROTK (as per the question), the equivalent scene is in "The Two Towers" book.