The Japanese people (日本人, nihon'-jin or nippon-jin) are those who typically speak Japanese language, are born in Japan and live, age, and die in Japan with Japanese citizenship and name. Very few are originally from outside Japan. The identity as ethnic Japanese and race is very little.
Japanese people usually have black hair and brown eyes and compared with Westerners, are shorter and thinner.
The question of Japanese national identity is tricky. A number of ethnic Korean born and living in Japan regard themselves as Koreans not Japanese, partly because they do not hold Japanese citizenship. Other minorities have ambivalent feelings. Okinawans may distinguish themselves from people in mainland Japan. Theres a small population of a native race called the Ainu, living in Hokkaido who retain their own identity just like the native Americans in the US do.
The origin of the Japanese people is a controversial topic among ethnologists. The most accepted theory is that about half of Japanese are from China via the South path and the other half are from the Mongol via the North path. There is some evidence that suggests some of the ancient tribes of Israel may have settled here.  
Jap is a slang term with a strongly negative connotation. Japanese have a strong sense of isolationism and social cohesion, referring to foreigners as "gai-jin" (outside person). Ironically, when in America, Japanese sometimes refer to Americans as gaijin and are surprised if asked whether the term might apply to themselves during their visit.