Anywhere from the horizon in to where the water's color changes because the bottom is visible. This of course started as a nautical term, and staying in the offing is important for navigational purposes. In this sense, it is first attested in 1627, coming from off-shore -- the modern idiom of the likely near future is from 1914. Incidentally, off itself is a derivative of the preposition of, in the sense of away from, not fully established as a separate word until Late Middle English.
The shore was quiet at dawn, with a couple jogging along the beach and a single trawler slowly chugging to windward in the offing.