What does the saying sorry about the inconvenience mean?

This just means that the person, usually on behalf of an organisation, will offer an apology for the consequences of something which was not your fault and beyond your control. An example would be where a mobile phone service provider temporarily had to cease providing connections due to a technical hitch and as this meant you could not receive or make calls for a short time, they are sorry for the inconvenience this would have caused to you.