From the 1880s until the 1930s, anarchist activity in the United States persisted, despite the repressions of the initial Red Scare. Radicals like Leon Czolgosz and Giuseppe Zangara terrified the American people through their violent attempts to assassinate American presidents. Two notable anarchists, Sacco and Vanzetti, were executed in the 1920s despite very flimsy evidence for any criminality.
From what I can gather, these activists were almost exclusively Catholic, continental European immigrants or the children of such immigrants, and xenophobic attitudes toward newcomers from Southern and Eastern Europe were closely tied to fear of anarchists. In addition, anarchists who did commit acts of violence seem to have been independent radicals rather than agents of any kind of revolutionary cell.
What did anarchists in America hope to achieve? Did they believe the assassination of a handful of politicians would actually bring about a society free of anarchy, or did they hope that such acts of violence would bring attention to the anarchist cause and instigate some sort of revolution?
This sort of tactic (shooting a president, stabbing a princess, bombing a parliament, etc) wasn't the 'first choice' for anarchism, to perhaps over simplify things. It has gone down in history as 'Propaganda of the Deed'. Broadly speaking, there is an emphasis among many anarchists, both today and in the past, in leading by example: you shouldn't just talk about what should be done, you should do it.
There's debate about where to trace the origins of anarchism, with some going all the way back to ancient Greek democracy - this isn't entirely wrong, I think, but I'm just restricting this to the mid to late 19th century. Anarchism started to grow during this time in the labour movement, both in actual unions of workers, and in smaller groups focused on propaganda (keep in mind that they might sometimes be referred to as 'federalists', as they were sometimes known as. Federalism is a key concept to anarchism, but almost all texts I've read will just use 'anarchists'). To cut a long story short, many of these organisations and groups were met with some pretty serious repression in a lot of places. Without the usual route of organising amongst workers, and with something as simple as distributing pamphlets often being a challenge, a few people (not many, numerically speaking, but the image has stuck, for reasons I won't go into) decided that the best thing to do would be to commit some high-profile attacks. The reasons vary, but to try and pull a common thread out of it, the intention was to inspire/awaken the masses, or something along those lines. I don't