Can someone explain what the 其 in 順其自然 means?
其 is referred to 'it' as in your translation. However, 自然 here does not necessarily mean the literal meaning 'nature'. Instead, it refers to the natural tendency of any subject you're talking about. If you see a child growing as he/she prefers to be rather than pushing him/her to be, 其is the child and 自然 means 'without intervention'. If you let something develop without attempting to change its route, 其 is that thing. In old Chinese, 其 as a personal pronoun is only one of its many senses.

What's more, it's a Chinese idiom, not just Cantonese.