"Taiwan independence" means different things to different people.
In a China mindset , it is used in the sense similar to that of "Tibetan independence movement", with the premise that Taiwan is part of China (though they know actually it is not), and separatism attempts are condemned.
For many Taiwanese people, the word and the movement doesn't make sense, because Taiwan (ROC) is already an independent sovereign. (Despite having only few diplomatic relations and not having a membership in UN.)
For some Taiwanese people, who seek for unification with China (about 7% of the population), "Taiwan independence" means the opposite of unification.
For some "Taiwan independence" advocates, it means "independence from ROC", with the goal of replacing ROC with a proposed State of Taiwan.
What are things to be done, if Taiwan people (supposedly) reached a consensus to achieve "Taiwan independence" or "establishment of State of Taiwan" that is independent from the ROC?
Edit: What does the Taiwan independence advocates wants to solve? What will they do to achieve it?
For example: adopt a new constitution, renaming the country...
"Taiwan independence" is a bad choice of word, but it is used all over the place in Taiwan news or Taiwan internet community, and many people are hoping for an "Taiwan Independence" to come some day, there is a high call for "Taiwan independence". The problem is that we don't know clearly what it is.
The reason that the idea of "Taiwan independence" attracts many Taiwan people is that 1. Repulsion against China. 2. The name of Taiwan's government is Republic of China. 3. Many people feel repulsed to be called Chinese.
Survey (2016) shows 59% identifies themselves as Taiwanese, 4% Chinese, 33.6% both, 4% didn't answer.