Yes, this term is used to describe the boring life that people lead when they work in the city in some boring, repetitive job adn they feel trapped. They feel they just work hard for some boss and don't really enjoy themselves, or make any progress. They feel like rats who have to race against each other all the time.

You can both speak and write this phrase, and you can find it sometimes in magazine articles for business people, or in books about how other people conquered their problems. Besides the meaning Ruthi gives, it can also mean "to feel like you are in a constant race with other people for money or power" https://dictionary.cambridge.org/dictionary/english/rat-race Examples: How to not get caught up in the rat race. I got so tired of the rat race, that I quit my job and moved to the countryside. Don't go into politics unless you like the rat race!