Taiwan is a small country next to China. Although people on both side speak the same language, the culture and government system is different. China, officially the People's Republic of China, is a sovereign state. Taiwan, however, is democratic. The Taiwan government originally based on mainland China, but was defeated by People's Republic of China, and moved to Taiwan.

Officially, Taiwan and China is in war. We never signed up armistice agreement. Taiwan politicians can be separated into two groups. One believe if we stay close to China, we can have better economics. A few of them even want to unite with China. The other group believe we should stay as a country of our own, and China government hates it.

With those background information you can see, making a economic agreement with china is sensitive to people, but the current government tried to pass it without standard procedure in congress. This is why people are so angry about this.

Technically, the situation is similar to the two Koreas, it's two Chinas at war, at least the mainland has never given up of uniting China, or conquering Taiwan.

Since the 60s though, after realizing military action against Taiwan was too risky due to US protection, the issue has been left alone. But some voices have raised since the 90s to unite Taiwan through political/economic means, like Hong Kong and Macau. Uniting Taiwan is a national pride issue for a lot of Chinese people, so there is political capital to be gained.

On the Taiwan side, it is a rich country, and people in general prefer their current lives, thus see no reason to be "united". There are some business people/politicians who benefit from closer ties with mainland, but they are the minority.