If you need a break from the rat race, it means you've had enough of your busy, repetitive work life. Imagine a harried businessperson rushing to get to the office — that's the rat race.
Experts aren't sure about the exact origin of the phrase rat race, although it seems to have started in the United States in the 1930's. If you imagine a rat struggling to survive on the city streets, or a lab rat running through a maze to find a piece of cheese, you'll get a pretty clear idea of the meaning behind rat race. If it helps, picture the rat carrying a little briefcase.