When English speakers refer to “famous last words,” they are often using a kind of sarcastic tone that means, basically, that a person's statement might be foolhardy, or not well thought through. Generally, the speaker is trying to communicate to another person that an idea might be “fatal” to them, usually in a figurative use of the word. For example, if cyclist says “this trick is really easy,” and someone else responds by saying, “famous last words,” the speaker is implying that the motorcycle trick may not be as easy as the cyclist anticipated. The idea is that the words that the person has just said, in this case, the person attempting the motorcycle trick, will be his or her “last words.”
The above is the most frequent use of the phrase “famous last words” in English. There are, of course, compilations of the famous last words of many celebrities and notorious individuals in English-speaking societies. These are cataloged into books or other literature. When English speakers use the phrase “famous last words” on its own, this is usually not what they are talking about.
It’s important to note that when English speakers use this expression, they are not always talking about physical danger, as in the example of the motorcycle trick above. This phrase can also be used to describe something with a more abstract danger. Someone might say to someone else “I feel confident buying this million dollar house. The market will only go up.” Another person might say “famous last words” to indicate that the prospective house buyer will likely fail spectacularly, and lose a great sum of money on the deal.
In addition to the above uses, the phrase can also be used in a business context, to refer not just to one person, but to a team of people, or an entire company. An executive or other staffer might say to a group of people “We are going to focus 100 percent of our energies on pursuing this one very important client.” If someone greets this proposal with the phrase, “famous last words” they are indicating that they feel this strategy will not pay off for the company or business. This is how the phrase usually works to express skepticism or concern, usually in a slightly humorous way. Indeed, some speakers may even use the phrase about themselves, as in: "These may be my famous last words, but I believe I will win this election."