If you make a mistake and it causes a problem:
Suppose a simple but useful example: You put a file in the wrong folder, and someone couldn't find it later on. That person comes to you wanting three things:
So, you might say "Oh, I must have put that in the wrong folder (1, 2). Sorry about that (c). From now on, I'll just keep the folder open while I'm looking at the file so I know where to put it back (2, 3).". Vu might respond "Oh that's ok, the file kinda belongs in this folder too.", which is basically false, but serves as an acceptance of the apology by removing the original complaint. You might then change the topic to some small thing worth saying like "Oh, by the way, did you get the May report ok?", allowing the conversation to end smoothly, on something that is going smoothly.
If vu's original request for an apology was aggressive, vu probably secondarily feels guilty, ashamed, or tense. A solid apology on your part (as opposed to an excessive apology that ends up seeming sarcastic) prompts vu to essentially apologize for the aggressiveness, allowing him to get rid of his secondary feelings, making the interaction clean, saving face. Try to generally recognize when you should accept someone's "offering" since it also helps vu in a necessary way.
This kind of conversation comes automatically if you have a certain ethical orientation: