Many people believe that Karate started in Japan. This is misleading. The Ryuku Islands, which are now politically tied to Japan without being part of the mainland, developed a fighting style in the 14th Century under the Influence of the Chinese. This was not introduced into Japan till the early 20th Century.
Of course there is a lot of pre-history to this. The Chinese martial arts that influenced the Ryuku Islands date back many centuries. They may have come from India centuries before that. The exact point where Japanese Karate separates from Chinese Kung Fu might be difficult to pinpoint stylistically; it helps to point to historical events (such as the first introduction to a country) in order to make find some dividing lines.
Karate is a striking art, using punching, kicking, knee and elbow strikes, grappling, locks, restraints, throws, as well as open hand techniques. It growing popularity in early 20th Century Japan may have been political; the ruling powers at the time were pushing Japanese militarism, and personal combat systems were being promoted as noble pursuits.
Karate did gain some influence in the west over this time. But it was not till after returning American Soldiers from the Second World War and Korean War that the martial art really gained popularity. Karate received a far bigger wave of popularity in the late 60s and 1970s when films featuring other martial arts appeared in the United States. The popularity of these foreign films was so influential that Hollywood soon started incorporating martial arts in many action films.
In 2016 it was decided to introduce Karate to the 2020 Olympics. This is highly appropriate as these Olympics will take place in Tokyo, Japan.