The idiom “at a loss” is used to mean that someone does not know how to respond to something. It is most classically seen in the phrase “at a loss for words,” which indicates that a person could not think of anything to say. You may hear or see this common English idiom used in a number of ways, and some people regard it as a cliché which should be avoided because it is so frequently used.
In the sense of “at a loss for words,” this idiom usually means that someone could not come up with an adequate verbal response to a comment or event. For example, someone who is surprised or startled might not know what to say, as might someone who is shocked by an event. People may also use this idiom to indicate that they didn't understand something, as in “I was at a loss for words after his last comment.”
People sometimes use the phrase in a somewhat derogatory way, to suggest that someone said something so idiotic or offensive that those present were at a loss for words. They may also use the idiom to describe emotional situations in which they were not really sure how to behave. Many people, for example, find themselves in this situation when approaching people at a funeral or memorial service, because they feel that phrases such as “sorry for your loss” are trite or meaningless because they are so overused.
More generally, one can be at a loss of response in general, not just words. After a film ends in a startling way, for example, the audience may not know how to respond. Likewise, protesters might feel this way after a march, uncertain about what to do now that they have reached their destination.
This term is also used in a slightly difference sense in the financial world, to discuss a situation in which someone is taking a financial loss. Classically, it is used in phrases like “I sold my assets at a loss because I was worried that the market would get worse.” When someone buys or sells at a loss, it means that he or she is taking a loss in the process, so people usually only embark on such an endeavor because they fear an even greater loss if they don't act quickly.
