Blue talk is language or a topic which is not fit for polite conversation. It is typically characterized by the use of words which are considered profane, along with discussions of topics which are deemed offensive. What qualifies as blue talk varies, depending on the culture and the company one is keeping. As a general rule, if one is not sure about whether or not something will be deemed offensive, it is better to remain silent.
The use of “blue” to describe something profane dates from around the 1800s, but the origins of this use of the word are a bit unclear. Supposedly, prostitutes in France were forced to wear distinctive blue dresses in prison to make them easy to identify, and this might explain it, but this claim is difficult to verify. Blue is also used in a number of other ways to refer to concepts besides the actual color blue, such as depression, and the roots of these meanings are sometimes equally obscure.
Whatever the origins of “blue” as in “profane” might be, people in the United States were certainly referencing blue talk by the 1840s, and the word spread to other English-speaking corners of the world very quickly. When a lot of blue talk is going on, someone might be said to be “turning the air blue,” but, curiously, when someone “talks a blue streak,” it just means that he or she talked very quickly, not necessarily profanely, although when someone "curses a blue streak," he or she is both talking quickly and being offensive in the process.
Historically, blue talk around women and children was especially frowned upon, and conversation in general tended to be more coarse among the lower classes than among the upper classes. While these tenets still hold true in many societies, the rules about acceptable conversation have changed radically; at one time, for example, women were not encouraged to participate in political discussion in the United States, but now they run for President.
Different people have different personal values, especially when it comes to language. Some people, for example, drop f-bombs left and right in their conversations, while others prefer to reserve strong language for especially trying situations. Crude language such as slang terms referencing genitalia may also be frowned upon in mixed company, especially when such language is being used to describe someone who is not in the room. Topics which are acceptable in some households are taboo in others, and words which have little important to some people are deeply offensive to others. Being aware of the need to be sensitive can help people navigate social situations more easily.