This expression means "What is going to happen to the world?" It expresses your disapproval of something. Use it when you notice a negative trend in society.
For example, you can ask "What's this world coming to?" if you hear about:
- horrible news stories
- children behaving much worse than they did when you were younger
- rising prices
- movies that are very sexual, violent, or dumb
"What's this world coming to?" is a rhetorical question, which means that you don't expect anyone to answer it.