Why was it so important for the Americans to win the revolution?
There are many possible ways to answer this question.
To begin with, you can say that it was very important to some of the leaders of the Revolution because losing might have cost them their lives. We do not know how vengeful the British government would have been if the colonists had lost the war. It seems likely, however, that some of the leaders, at least, would have been executed for treason.
We can argue that it was important for the colonists to win the war so that they could be independent. We can say that this was important to the country. This is because winning the war meant that the Americans would now be able to govern themselves. They would no longer have to be subjects of a distant government that did not respect their rights. By winning the war, Americans gained political and economic rights and therefore became freer and richer than they would have been if they had lost.
We can also argue that the American victory has been very important for the world as a whole. It is possible to argue that the world would be much less democratic if the colonists had lost the war. The United States has been the inspiration to many democratic countries. It has done much to help the cause of democracy and justice in the world in the 200+ years that it has existed. If the colonies had not won the war, these things would arguably never have happened.
However, you can also take a contrarian view and say that it was not important for the Americans to win (except for those few Americans who would have been executed if they lost). We can say that America would eventually have become independent anyway. We can look at Canada and see a country that did not fight Britain for its independence but which is still as democratic and free as any country. If the Americans had lost the war, the country would (we can argue) have continued to grow to the point where Great Britain would have realized that it needed to grant the colonies independence just as it did with Canada.
If I were the teacher who assigned this question, I would accept any or all of these answers. Which one or ones makes the most sense to you?