This is an expression for disagreeing with someone or stating a negative opinion. It's polite-sounding, and doesn't seem too forceful. You can use it when you want to disagree with someone's opinion, like in this example:

Yeah, I don't know... the privacy issue doesn't really concern me too much.

In the example above, the speaker isn't really disagreeing with her friend's opinion. But she's saying something a little negative. She's saying that she doesn't like the pants. So she states her opinion in this polite way, by beginning with "I don't know."