The Taipei Economic and Cultural Representative Office (TECRO), sometimes known as Taipei Representative Offices, are de facto embassies and consulates of the Republic of China (Taiwan) in countries that do not have official relations with the ROC because of relations with the People's Republic of China, but have nevertheless established trade and "cultural" relationships. These establishments use the term "Taipei" instead of "Taiwan" or "ROC" since the term "Taipei" avoids implying that Taiwan is a different country or that there are "Two Chinas".
By calling these offices TECRO, the ROC gets around the diplomatic language surrounding recognition by these states that the PRC is the One China by stating that their aim is to "with the aim to promote bilateral trade, investment, culture, science and technology exchanges and cooperation, as well as better understanding", rather than diplomatically represent the ROC abroad.
Despite its name, TECRO does everything that a normal embassy or consulate would do, like issuing visas. Offices from other countries, such as the American Institute in Taiwan or the Canadian Trade Office in Taipei, are similarly established in Taiwan.
It is also worth noting that Hong Kong also represents its interests abroad by establishing Hong Kong Economic and Trade Offices (HKETOs) and does its visa work there also. However, the Embassy of the People's Republic of China represents Hong Kong's interests in countries or regions where there is no HKETO.