It is rather difficult to make the argument that Rachel Carson's book in fact changed American History. It has served as a reference text for many folks that are currently working to change policy and practices in the United States to be more "green" or environmentally friendly. You could argue that it played a role in stopping the use of DDT as a pesticide, but farmers and others still use tons of chemicals that are likely harmful in many ways so it hasn't eliminated or even seriously impeded the use of various chemicals all over the country.
Perhaps one could argue that its popularity (limited though it was) was enough to raise questions in the mind of many who read it and hopefully led to positive changes. But it is very difficult to connect a book (any book really) to specific and definite changes in history.
With the kinds of environmental abuses and neglect that was taking place in the 1950s and 60s, it was inevitable that a green movement of some sort would start, just as in the 1850s, it was inevitable that an abolition movement would grow. In that time period, the book Uncle Tom's Cabin sold hundreds of thousands of copies and changed minds, increasing the size and momentum of the anti-slavery movement.
Silent Springdid something similar. It took a fledgling movement and an unknown debate topic and brought it into specific relief. It made it into a national discussion, and there were magazine and journal and scientific and political responses to it.
Did it change history? Yes it did. Just not all by itself. The car was already running, her book just stepped on the gas.
In my opinion, this book kind of started the environmental movement that is such a big part of the American political and social scene today. The book did help get DDT banned, but I think it was much more important than that.
The environment was not really seen as an important topic before the book was published. Since then, it has become one of the most important issues. Nowadays, you have people buying the spirally light bulbs and hybrid cars. You also have a huge conservative backlash against environmentalism.
So, to me, the book helped cause the green movement and the backlash against it that has made green issues part of our current "culture wars."
The biggest change that came about as a result of Carson's book, and one of the reasons that the work is still as popular as it is today, is that it generated an awareness of the problems that we are causing to the environment through the use of pesticides such as DDT. The thing bout her work is that, although it was written in the 1960s, we still are facing many of the same environmental issues that she forewarned us of. In one section, she paints an image of an imaginary town where birds once sang and children played that is now dead and lifeless, the people and animals sickening and dying, all because of a white powder that settled over the area. This white powder was DDT (a pesticide) but it can easily be any pollutant man creates. Carson's work is pivotal because it made the general public more aware of the damage it was causing to the environment and the ramifications of that damage on the future.