I have a naive question : ) If by Universe they mean everything outside our Galaxy how could it possibly be defined by size? Are they only speaking of the portion of the Universe that we can either see or measure from Earth or by other means? I've always considered the universe to be infinite. Am I missing something?
Our universe (and there may well be many more universes besides our own) isn't infinite, but there also isn't anything "outside" the universe - the universe is defined as space itself, but space itself has been expanding since the Big Bang. There's no "empty space" outside the universe it's expanding into, though.
I realize it all makes your brain hurt...try reading any of the books from Brian Greene or Michio Kaku.
Here is what you are missing. According to Greene, mentioned above, the radius of the universe is 25 billion times bigger than the Hubble radius. The Hubble radius is as far as the Hubble telescope can see, which is nearly all the universe that can ever be seen since the rest of it is leaving us faster than the speed of light. That is, we can see a grain of sand and take that for the entire earth--similar relative scale.
No, the universe is definitely finite, though the 'radius' of a 15 billion year old universe might be 40+ billion years thus the horizon is beyond our ever getting information from it. For all we know, the whole 'shebang' may be contracting at some where/when out beyond our information horizon, and in a few million or billion years, we'll be 'incorporated' in the 'renormalization' (collapse).
Yes; "detectable" universe would perhaps be a better terminology. We can only see that portion of the "total universe" that is within our light horizon (the portion of it in which the expansion of space is appears to earth to be at speeds less than the velocity of light.)