To quote the manual:
Special Ability: Hurry Production
You can expend a Great Engineer to create a sudden burst of production in a city. The production is immediately applied to whatever is presently being built in the city – unit, building or Wonder. This will usually be enough production to immediately finish all but the most massive Wonders, and it will drastically shorten their production time.
I had a great engineer during modern times, and using it to help produce the Statue of Liberty (1200 prod needed) yielded 750 production. Letting it help along for a Stock Exchange immediately finished this building (650 prod cost).
I assume that the amount of prod. generated is somehow game-stage related? Are there any known specific rules?