Something about it still doesn't make sense to me. If the universe is only about 14 billion years old and it is 30 billion light years away, wouldn't the distance between us and it have to be increasing faster than the speed of light?
I'm somewhat exhausted from work, so maybe I'm just missing something here...
That's actually what's happening. The universe is growing faster than light. Look it up.
And beyond that, it's currently accelerating due to dark energy. Dark because we don't know wtf it is, but it's uniformly causing expansion of the universe faster than it can collapse in on itself from gravity. Which means some sort of uniformly distributed negative energy. The discovery of its nature is one of the biggest mysteries in current physics, and will probably revolutionize it and our technology in pretty massive ways.
But anyway, yes. This is also why, given sufficient time, the farthest stars and galaxies in the sky will redshift to nothing. The Cosmic Microwave Background radiation, which you see in the sky in the microwave range, around what an analog TV receives, originally consisted of high energy gamma rays created as the universe cooled. And as the universe continues expanding,
it's expected it will redshift to nothing in about 1 trillion years.So when it is said 'the universe is 56 billion light years across,' it's really just shorthand for 'the visible universe is 56 billion light years across.' And yet, this is 'the universe' as far as we are concerned. Without travelling faster than light (which, thanks to Einstein means travelling backwards in time), you cannot run fast enough to get past that 'edge' of the universe. Anything slower than the speed of light, and the edge will recede due to the passage of time; at the speed of light, and the edge will stay at the same place. So in short, yes, there is probably more 'stuff' out there; but we can never interact with it through any force, light, spacecraft, or otherwise. And as such, it is outside of our universe.
It doesn't make any sense from a classical perspective; which is why, to understand it, you need to visualize space-time as a singular entity.