There are many different ways that one could answer this question. I would suggest that you look in your book or your class notes to find out which answer your instructor expects you to give. Let us look at some possible answers.
One could argue that the demonstrations at Tiananmen Square were not important at all. These demonstrations were meant to push the Chinese Communist Party to allow the country to become more democratic. Since the party did no such thing, we can argue that the demonstrations were not important.
Alternatively, we could argue that the demonstrations were important because they made the Chinese Communist Party more intransigent. The demonstrations (along with things like the unrest that led to the collapse of the Soviet Union), made the party feel that it could not give in to the people on issues of democracy. If we look at it this way, the demonstrations were actually counterproductive because they made the party less receptive to the idea of democracy. This would mean that the demonstrations were important because they helped to make the Communist Party more conservative and authoritarian.
We could argue that the demonstrations were important because they showed the world that the Chinese Communist Party was a ruthless organization bent on maintaining its power. The demonstrations showed that the party was willing to kill large numbers of unarmed people simply because they were protesting. The demonstrations, then, showed the party’s true colors.
Finally, we could argue that the demonstrations were (and are) important because they show us how important democracy and human rights are. The protestors were willing to stand up for what they believed in and were willing to risk their lives for democracy and rights. In this way of thinking, the protests were important because they remind us of the importance of things we often take for granted.
Again, however, you really should check your own class materials because there are other possible answers and there is no way for us to know what answer your instructor expects to see.
It was the first visible demonstration of the will of the people to break free of their social and political shackles. The Chinese government could no longer hid behind their "Great Wall".