“I got caught without an umbrella.”
You showed up to work soaking wet because it started raining and you didn't have an umbrella. A co-worker sees you and asks what happened. You say this to explain how you got drenched.
I got caught without an umbrella.
To "get caught" in the rain means that you are outside and it starts raining suddenly, before you can get inside or get an umbrella.
The phrase "get caught" is interesting. It's connected to the phrase "catch someone":
A police officer chased the thief down and caught him.
From that meaning came a secondary meaning, which means to see someone doing something that they wanted to hide or keep secret:
I caught Ed watching YouTube videos in his office the other day.
Tiger Woods got caught cheating on his wife with a restaurant hostess.
Another meaning came from that which is to be suddenly put in a situation that you're not prepared for:
Neal got caught unprepared by the interviewer's question.
This is the sense that "get caught in the rain" is closest to. It means that you are unprepared for the rain when it starts.
Use this phrase when you don't have something that you need, but you do an action anyway. Some quick examples are:
We had to eat dinner without any forks or spoons.
I can't work without a computer.