It's good manners to apologise when you make an error that causes inconvenience or delays someone else's progress. Sorry is an acknowledgment that goes some way to alleviating any frustration or anger you may have invoked in another. Sorry says I didn't mean to do that, please accept my admission of unintentional wrongdoing.
Like many good gestures though, the apology has been watered down and abused where it is often used as a disclaimer or shield against wrongdoing. People will do something wrong intentionally then use "sorry" as a get out of jail free card. I experience it typically when conducting business. When I started out I had a website outsourced to a web development company. When I would ask my site administrator to correct something simple that should have been right in the first place, often the response would take a matter of days rather than hours. The correction too would only come after numerous follow ups and the occasional inclusion of the web company owner's email address in the cc line.
Eventually I would get a call or email from my host company along the lines of: "Hi Lishen, sorry for the delay, but we had a backlog. The server issue has now been resolved..." A delay numbering in days shows a priority list where I was near the bottom. The fact that it was resolved eventually provided little consolation. This wasn't OK with me because I was paying top dollar for an uncomplicated site. Every time my support guy would be very apologetic when he eventually got back to me, yet when I was frantically trying to contact him I was being intentionally ignored. The apology therefore meant nothing.
I even have a friend who cuts things finer than a nano laser because he knows he has a string of buddies (me included) to bail him out. He would purposely not buy an essential like a computer but spend the money on modifying his car instead, for instance. Why? Because he could access his private email from work and if he ever needed something printed urgently after hours he had Lishen to lean on. "Hey man, so sorry to trouble you, but I have a hearing tomorrow and need to print some emails... so sorry but this just came up. I owe you big man." He's popped by unannounced on Sunday nights, Saturday mornings, during the middle of lunch - you name it. (I've known the guy since I was eight, so cutting ties is easier said than done.)
A real apology is a polite impromptu reaction expressing regret and a desire to make things right after initiating an outcome you didn't anticipate and intend. When a person violates, inconveniences or retards you with the pre-meditated intention of apologising afterward, the essence of the apology is destroyed. A pre-meditated apology means nothing because it means that the wrongdoing was intentional.