Well, a history lesson here :)
ROC was the government of China before PRC was founded. Kuomintang Party was the founding party of ROC that turned over the Qing Dynasty and governored China from 1912 until 1949. But they lost the civil war to the Communist party in mainland in 1949 and fled to Taiwan.
Kuomintang continued to be the only dominant party in Taiwan until 1980's. They claim that ROC is the legit representative of the whole China (including mainland). US and most of the western countries did not recognize PRC and let ROC be the representative of China in UN. However, this changed in 1971 when PRC gained more votes from other countries to replace ROC in UN. ROC and PRC both insisted the one China policy, and thus ROC decided to quit UN and rejected a proposal to let Two China co-exist in UN.
However, things changed again when the opponent party in Taiwan grew stronger and took over the government in 2000. The opponent party is a local party supported by the native Taiwan people (still, they moved to Taiwan a few generations ago from mainland). While Kuomintang Party is supported by most people who moved to Taiwan after they won the world war II and recovered the Taiwan after Japan gave it up. These two parties continue to fight and they disagree on "One China" policy. The local party wanted to be independent but they cannot, since PRC will start the war if they do claim the independence. Officially, the end of civil war of China has not been declared.
Officially, the ROC constitution claim Mainland China and even Mongolia to be part of ROC. However, their power can only reach Taiwan and nearby islands. There are a few small countries who still recognize ROC (Taiwan) as the representative of China and tie diplomatic relationship with ROC. But most of the countries maintain the official diplomatic relationship with PRC and an unofficial relationship with ROC (Taiwan).
To prove what I said, I include a set of Taiwan's map stamps (in Scott under China 1157-1162). You can see that their map of China, which include mainland China and Mongolia (they don't recognize the Independence of Mongolia because they let Mongolia go under the pressure of Russia but Russia turned to support ROC's enemy -- the communist party). There are 4 Chinese characters on the maps meaning "recover the mainland".
Stamps are a history book, indeed.