★The term“对不起”is the formal and upgrading saying of the term“不好意思”. It is used when a serious trouble is caused due to your fault. For instance, you should use this term in the situation that you offend a colleague or hurt your girlfriend. And it shows your sincerity when you say it with a depressed expression. If you say“对不起”without emotion, it would be superficial as saying“不好意思”.
(“起”与“气”的发音相似,我们排版时忙中出错把“起”与“气”搞错了,现已更正,感谢Alec (wangyx1@****.net)指正的错误,在此也对大家说声“对不起”。)