Imagine that work or school are like a race. If you stop to take a rest, everyone will keep running ahead, and if you want to continue you'll have to run extra hard to reach where they are. In a race, to "catch up" to someone means to reach where they are after starting out behind them.
At work, when you start a new job or come back after a vacation, you have to "get caught up". This means to work hard so that you can figure out what's happening and get ready to work.