I was wondering what is the farthest the best optical telescope can see into outer space from Earth. What causes them to see so far?
"How far" is kind of an odd way to measure how good a telescope is.
The visibility of a distant object depends on how bright it is, not only how far it is.
How far can you see with the naked eye? About 10.5 billion light-years. There was a "gamma-ray burst" that was at this distance and would have been visible without a telescope (though there is no evidence that anybody actually saw it)
There are galaxies that are 32 billion light years distant. Further than this is the "surface of last scattering" which we see as a uniform glow of light reaching us as a relic from the big bang. This is about 42 billion light years away, but you don't need a particularly "good" telescope to detect it, you only need a radio telescope. However the surface of last scattering was so bright that it doesn't need a very big radio telescope. You can't see any further than this, since this is almost back to the start of the big bang.