Republic of China on Taiwan is a political term as well as discourse regarding the present status of the Republic of China. It is proposed by former president of the Republic of China Lee Teng-hui, the first Taiwanese President. During his presidential tenure in 1995, Lee visited his alma mater Cornell University and mentioned this term for the first time when delivering an Olin Lecture.
The term is one of the several terms regarding the Republic of China, and is not exactly about Taiwan independence. The term was later included in the Four-Stage Theory of the Republic of China as the third stage from 1988 to 2000 by President Lee's successor Chen Shui-bian.)
Before Lee Teng-hui coined the term, the officials of the Republic of China had always used the state's official name "Republic of China". Therefore the term was regarded as a breakthrough.
In regards to the origin of the term, Lee Teng-hui explained in 2005 during a lecture in Lee Teng-Hui Institute that, following the World War II, Chiang Kai-shek's forces temporarily occupied the island of Taiwan under the direction of Supreme Commander for the Allied Powers Douglas MacArthur, and because both the Treaty of San Francisco and the Treaty of Taipei concluded afterwards did not explicitly specify to whom Japan renounced the sovereignty of Taiwan for, the legal status of Taiwan has become undetermined, and therefore he coined the term "Republic of China on Taiwan".