I know some people with 4 octave voices that sing purely for fun and yet others with a mere (comparatively) 2 octaves who are serious singers. Why is there such a big difference in this? Is it to do with nature, or nurture, or both? Are some at an advantage because of their parents' genes? And how can you make your voice change its range?
It's a bit of both. You have what you have, genetically, and some people have a great range of 4 octaves (rarish), compared to a lot who have a decent two octave range. The latter is enough for most stuff, and changing key helps! With some training, another couple of tones at one end (or both) is possible, but quality of voice can suffer at each end.
Increasing range happens with lots of use, and also being aware that certain vowel sounds are easier to sing at the edge of one's range.
When singing solo, most songs can be accommodated with a couple of octaves, especially with any aforementioned key change. Problem comes when singing harmony with others whose ranges are also limited. Occasionally, a key which fits all cannot be found, as I sometimes find in various ensembles. Or the guitarist can't/won't change key...