When you're speaking with someone you don't know well, it can be polite to say "I'm sorry" before asking a question. For example:
I'm sorry. What was that?
I'm sorry. Do you know where the restrooms are?
You can also apologize for problems that aren't your fault.
I'm sorry. I didn't catch what you said.
The implied question here is "Can you say that again?"
The reason for apologizing in these situations is that you're supposed to listen and pay attention carefully when speaking with people who you don't know well. However, when someone says "I'm sorry" in this way it probably doesn't mean that they feel truly sorry.