The coffee table originated in England during the Victorian era. The original tables were not as low as what we know today. They were about 27 inches high and made of wood.
As coffee tables became popular in 20th century, it was not unknown for tables (even antique tables) to have their legs shortened for this purpose. This could give the idea that they were actually around longer than they really were.
Their main purpose is to have a place to set down a beverage while entertaining. They often come as a set with accompanying end tables. Some people have even substituted other items as coffee tables, such as trunks.