The "bikini" was named after Bikini Island in the Bikini Atoll where they used to test nuclear bombs.
In 1946 Jacques Heim and Louis Reard introduced the bikini swimsuit while the U.S. was doing post-war nuclear tests.
They billed their new swimsuits "smaller than the smallest bathing suit in the world". This was in response to another one-piece swimsuit called the "atome" which was supposed to be the smallest in the world.
Bad pun alert: Since the bikini was even smaller than the atome and it was two pieces instead of one, it was said that the bikini "split the atome".
However, archaeologists have discovered wall paintings from Ancient Rome of women in clothing that looked like modern bikinis. This would mean that women may have been wearing bikinis a long time ago, before they were supposed to be invented in the 1940s.
(Sources: 1, 2)