Converse got their name from their inventor Marquis Converse. Marquis, started the Converse Company. In 1908 when they were invented they weren't really popular. They were made from rubber and canvas.
In 1920s they became special shoes for basketball, called the Converse All Star. They were promoted by players. After that they became the offical NBA shoes and they were popular with artists and musicians too.
These days, converse are less popular taht they used to be. The Company was sold to Nike in 2003, and now it seems to be more popular. In total 950 million pairs were sold by 2008.