It is mostly used in England. It is used mostly by the middle and upper class people and not by the working class person.
How you say" I beg your pardon" can communicate different things. When said gently it can mean "sorry I don't understand" or it implies that you need them to repeat what they said. If you say " I beg your pardon" with more strength and conviction it can imply you have said something that has offended them.
'I beg your pardon' is also a formal way of asking someone to repeat themselves.
That is, "I beg your pardon?" = "Could you please repeat that?"
May 7, 2019
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It is a more formal way of saying sorry. In English US context, it is not that common as it is being used in British English.
May 7, 2019
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In addition to the above two comments (as an apology or asking to repeat onself), in some situations (in the US) if said in a certain way, it can be used to express outrage or strong disagreement (while appearing civil).