As with many things in Christianity, there are words or phrases used which sound familiar coming from a secular perspective, but which have a different sense when used in Christianity. It is easy to misunderstand or get tripped up by these statements.
To ‘leave the World’ is not to leave everything here-and-now behind. Rather, it is to embark on a ‘revaluation of values’, to borrow a phrase.
In particular, to leave behind materialism and hedonism (cf. Stoicism) and instead put value on God (= the Good) and the Christ (= our connection or ‘Way’ to the Good).
Since the Christ has “come that they might have life, and have it more abundantly” according to Christianity (John 10:10 – i.e., it is our connection to the Good that allows for us to live a human life fully), to ‘leave the World’ is to see through those things which detract from a life fully lived, and instead to focus on the most important thing.
It includes, of course, self-discipline – the reigning in of impulses that are good in the short-term but have a net negative effect in the longer-term. More over-archingly, though, it involves a leaving of one’s ‘self’, which is to say, of an ego-centric way of habitually viewing things, and instead a focusing on the Good (which involves focusing more on the good for others).