The Enlightenment was significant because it helped to create the modern age in which we live. The attitudes and values of the Enlightenment are very similar to those we still hold today.
The thinkers of the Enlightenment wanted to use reason and the scientific method to improve society. They felt that they could make a better world by getting rid of outdated ideas and sticking to those social structures and ideas that were logically and empirically better. They believed that this allow progress to happen.
We, today, believe in most of these ideas. Our democracy comes out of ideas of the Enlightenment. So do our social sciences, by which we try to understand our societies. We continue to have the idea that we can determine, through the use of reason, how to improve our societies.
In these ways, the Enlightenment is significant because it gave rise to the attitudes that form the basis of our society.