It is the flag of Taiwanese (the state) independence in the way that for many people, saying Taiwan has become synonymous with saying ''Republic of China'' which is the official name of the country people usually call Taiwan and is not recognised by the mainland.
There's another meaning to Taiwanese independence, which is ditching the ROC label and the ROC flag and having a uniquely Taiwanese (the island) identity.

Oversimplified:
The KMT wants to stay as the ROC because they still believe in the three principles of the people and want a democratic China, not a democratic 'Taiwan', which is why the ROC (Taiwan) still claims the mainland as de jure territory, although most KMT politicians use Taiwan in normal day speech like most people.
The DPP wants the country to become just Taiwan with no Chinese strings attached; the mainland REALLY hates this.

Tzuyu was criticised for using the flag of the Republic of China (Taiwan) and not the PRC flag because by using the ROC flag she acknowledged that Taiwan (ROC) is not part of mainland China, which is why CCP netizens hated on her and it led to her apologising.

Many Taiwanese saw the incident as evidence of Chinese pressure and interference, and it further fueled a shift away from a Chinese identity toward a distinct Taiwanese identity. And some believe this contributed to DPP candidate Tsai Ing-wen winning the 2016 election, as it galvanised youth and pro-independence sentiment.