What does "I'm Sorry" mean to you?

I was just writing a condolences message to a classmate that lost a sibling unexpectedly and I was thinking about the phrase "I am sorry for your loss."  This made me think about how people have such a hard time saying "I'm sorry" when they've done something wrong, but they say "I'm sorry for your loss" even when they don't have a clue what the person is going through or even if they know them at all. I think that "I'm sorry" should be more used in our daily conversation. We need to change what it means to us. It shouldn't be just an admittance of guilt or wrong-doing. That's what makes it so hard to say. We need to change our perspective of the words. When you are giving your condolences to someone you are saying "I am sorry for the way you are feeling," even though I had nothing to do with what made you feel that way. I sympathize with your pain. Even though sometimes I think we NEED to admit our own short comings and admit that we messed up, I think we need to change our perspective of the words. We need to focus more on the other person's feelings and remember that it's all about them. I am sorry for the way you are feeling. That wasn't my intentions. I sympathize with your pain. It's not about me. Then "I'm sorry" may come alot quicker and more often in our day to day lives. What do you think? What does "I'm Sorry" mean to you?