What you should read:

The study of anarchist terrorism, both within the U.S. and globally, has become much more popular due the contemporary relevance of terrorism (as we, unfortunately, have been reminded again today). The following books are just a few of the best concerning anarchist terrorism and the American response to it:

Beverly Gage, The Day Wall Street Exploded: A Story of America in its First Age of Terrorism

James Green, Death in the Haymarket: A Story of Chicago, the First Labor Movement and the Bombing that Divided Gilded Age America

Timothy Messer-Kruse, The Haymarket Conspiracy: Transatlantic Anarchist Networks

Richard Bach Jensen, The Battle Against Anarchist Terrorism: An International History, 1878-1934

Paul Avrich and Karen Avrich, Sasha and Emma: The Anarchist Odyssey of Alexander Berkman and Emma Goldman

Although not concerning the U.S., I'd also recommend John Merriman's The Dynamite Club: How a Bombing in Fin-de-Siecle Paris Ignited the Age of Modern Terror

Finally, I would also suggest the relevant chapters in Martin A. Miller's The Foundations of Modern Terrorism: State, Society, and the Dynamics of Political Violence and Matthew Carr's The Infernal Machine: A History of Terrorism

How Big Was It and what Impact Did it Have?

While anarchism in the United States was certainly a fairly prominent ideology and movement at the turn of the century, the number of anarchists that supported or were willing to carry out terrorist acts--typically called "propaganda by the deed"--was relatively small compared to that of Europe. Anarchism and anarchist terrorists were probably most numerous and most militant in France and Russia, although even in these places law enforcement had effectively demolished anarchist terrorist groups by 1900. It was, in fact, this crackdown against anarchists in Europe during the late 19th century that led to a mass migration of European anarchists to the United States. A handful of these immigrants would come to play a significant role in bringing anarchist terrorism to the United States. Johann Most is perhaps the most notable of these European anarchist immigrants, as he became the most vocal proponent of terrorism, going so far as to publish his own weapons manual that taught anarchists how to build bombs.

Anarchist terrorists represented only a very small part of the broader anarchist movement in the United States, and many anarchists condemned the use of violence to achieve their goals. The vast majority, for instance, thought that Alexander Berkman's attempted assassination of the industrialist Henry Clay Frick actually set the movement back. Despite the relatively low numbers of active anarchist terrorists in the United States, the general American population and the American government were incredibly afraid of future anarchist attacks. To address these concerns, government leaders drastically improved law enforcement capabilities from the local to the international level (Gage's and Bach Jensen's books are particularly good on this point) Perhaps unsurprisingly, this improvement in law enforcement also saw a heretofore unprecedented level of government intrusion in the lives of many Americans--law enforcement personnel would, for instance, routinely sift through and open the mail of citizens at post offices, with effected citizens left none the wiser. At the same time, this improvement in law enforcement was incredibly effective at demolishing the American anarchist movement (as it had been earlier in European states) by about 1920. So, while this answer has been very, very brief, I think two of the most significant outcomes of anarchist terrorism in the US is, first, that it led to a massive expansion of policing/national security powers and the drastic improvement of law enforcement agencies in the United States. Second, and related to the prior point, the expansion of these policing and national security powers ultimately helped lead to the collapse of the anarchist movement as a major political and social force in the United States.