American Sign Language, usually abbreviated to "ASL", is the principal sign language in North America, including the United States of America (with perhaps 2 million people knowing the language), and English-speaking parts of Canada, as well as parts of Mexico.
ASL is also used to some degree in a number of other countries around the world, but it should be emphasized it is not mutually intelligible with the sign language used in the United Kingdom which is known as British Sign Language ("BSL") and is in fact quite different (ASL is in fact very similar to modern French Sign Language, and has about 60% vocabulary in common with it).
ASL has its own grammar, syntax and idoms, that are distinct from spoken English.
The language traces its origins to the 19th century, and many people attribute its early development to the Reverend Thomas Hopkins Gallaudet who was the first principal of the Hartford School for the Deaf in Connecticut, which is today known as the American School for the Deaf.
American Sign Language is of course principally used by the deaf and hard-of-hearing, and by their families and others to communicate with them.
Many families do use ad hoc sign languages to communicate with deaf children, but ASL classes are widely taught in secondary and postsecondary schools in the United States.
For those who wish to learn ASL at home, or perhaps brush on their skills, the Internet can be helpful - for example, you can find downloadable courses that teach it.