Taiwan has been effectively self-governed ever since the end of the Chinese Civil War in 1949. At the conclusion of that war, the Chinese Communist Party (CCP), led by Mao Zedong, routed the Kuomintang (KMT), led by General Chiang Kai-shek, the latter of which was forced to retreat to Taiwan.
Many know that China (the "People's Republic of China") today lays claim to Taiwan. Less well-known is that Taiwan ("The Republic of China") also lays claim to all of mainland China!
Official CCP propaganda will tell you that Taiwan has "always been" part of China. But that's not the case. Taiwan wasn't annexed by the Qing dynasty until 1683, which is relatively late in terms of Chinese dynastic history. Prior to that, it was populated by indigenous peoples and then the influence of Dutch and Spanish traders and colonists during the age of exploration. https://en.wikipedia.org/wiki/Taiwan#Qing_rule_(1683–1895)
Taiwan was later ceded to Japan at the end of the Sino-Japanese war in 1895 pursuant to the terms of the Treaty of Shimonoseki.
Japan continued to govern Taiwan until its surrender in WWII (1945), at which point it was transferred back to China. China instantly got into a Civil War as described above. The administration of Taiwan was always on ROC's side, however, which allowed it to serve as a fall-back point.
The point of the meme is this: If Taiwan is ever re-unified with the mainland, it will have to be through peaceful means. I could see that happening within the next 100 years or so, depending on political and economic developments on both sides of the Taiwan Straits. Though China's cracking down on political freedoms in Hong Kong has made Taiwanese more wary of that possibility than before.
An amphibious invasion by China, on the other hand, would be logistically difficult to pull off and incredibly costly and destructive. China has a large and powerful (though unproven) army/navy. Taiwan is smaller but no push-over and is armed to the teeth as well with much American weaponry. The Taiwan Straits are 80 miles wide, a distance comparable to that traveled by allied forces on D-Day. Taiwan is mountainous and could mount a guerilla campaign. There is no guarantee that the U.S. wouldn't enter the war on Taiwan's side, either.
Alternatively, China has the firepower to simply nuke Taiwan, but that wouldn't be in China's own self-interest, either.
These military and diplomatic calculations are what has kept Taiwan under self-rule for the past 70 years.
