Most of the time, it used as a way of "excuse me" with a slightly unfriendly tone. For example, if the cashier at the store doesn't give you the right change, you can say "I beg you pardon, but you still owe me 25 cents." Other times to use the term: If you didn't hear or understand someone, you can use it to express that fact to the speaker, but the more proper response would be "Excuse me." If you need to interrupt a conversation, you can use it to express that you're sorry for doing so. "Excuse me" may be a better option, though. If you accidently run into someone in a crowd or on the street, you can use it to say that you're sorry for bumping into them.