What do we mean by the observable universe?

It would be #1 because it would be the part of the Universe that we could see given that light has a finite speed, so any part of it that is farther away than it would be possible for light to ever reach us since the beginning of the Universe would never be observable to us. It would include those parts of the Universe that are obscured by dust or whatever making them within the span of the Universe that could be seen except we cannot see into that area because of the dust or whatever.