1.to tell someone that you are sorry that you have done something wrong:
I'm so sorry, I do apologize.

2.used when you are going to say or do something that might seem rude or offensive and you want it to seem more polite:
Forgive me, but I don't think that is relevant.
forgive me for asking/saying etc something also forgive my asking/saying etc 
Forgive me for saying so, but that's nonsense.

3.a) used to say 'sorry' politely when you have accidentally pushed someone or interrupted them:
Oh, pardon me, I didn't mean to disturb you.
b) used to say 'sorry' politely after you have made an impolite sound such as a burp
c) used before you politely correct someone or disagree with them:
James, if you'll pardon me, you've got it all wrong.
d) used to politely get someone's attention in order to ask them a question [= excuse me]:
Pardon me, can you direct me to City Hall?

4.a) used when you want to get someone's attention politely, especially when you want to ask a question:
Excuse me, can you tell me the way to the museum please?
b) used to say that you are sorry for doing something rude or embarrassing:
Oh, excuse me. I didn't know anyone was here.
c) used to ask someone politely to move so that you can walk past:
Excuse me, could I just squeeze past?
d) used to politely tell someone that you are leaving a place:
Excuse me a moment. I'll be right back.
e) used when you disagree with someone but want to be polite about it [= I'm sorry]:
Excuse me, but I don't think that's what he meant at all.
f) American English used to show that you disagree with someone or are very surprised or upset by what they have just said:
'You're going to pay, right?' 'Excuse me?'
g) especially American English used to ask someone to repeat something that they have just said [= pardon me]:
'What time is it?' 'Excuse me?' 'I asked you what time it is.'

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