There are a number of ways that this could be answered. Let us look at two effects this document had, one immediate and one that took longer to become evident.
First, the Declaration established that the colonies were truly trying to become independent. Up until that time, the rebellion had not explicitly been about independence. Even after the fighting started at Lexington and Concord, there were still attempts, such as the "Olive Branch Petition," to reconcile with Great Britain. The Declaration made clear that such attempts were over and that the war was about creating a new country.
In the longer term, the Declaration's effect has been to serve as a statement of America's aspirations. It has helped to define who and what we are as a nation. By setting out the idea that our nation is dedicated to the idea that "all men are created equal," the Declaration has helped to shape our history. It has given support, for example, to rights movements that range from abolition to gay rights. It has served as a national ideal that we have continued to strive to achieve.
In this way, the Declaration had important effects both in the short term and in the long run.