The chief aim of terrorism, as its name implies, is to instill fear, and a lot of us have inadvertently aided the bad guys by exaggerating the threat.
Of course, this isn't to say that terrorism is nothing to worry about. We all remember September 11, 2001, when airliners hijacked by terrorists killed several thousand innocent people in the United States. That was by far the single worst terrorist strike in world history. In the many years since then, fewer than 200 persons total have been killed by terrorists in the United States. For comparison, the United States has recently averaged around 16,000 non-terrorist-related murders every year (see e.g. the latest FBI crime statistics), which is itself smaller than the annual average number who die from influenza or traffic accidents.
Many of us tend to think of terrorists as foreign Muslim extremists, but most of those attacking the U.S. have been citizens or legal residents typically acting on their own or in small groups, and many have not been Muslim. The second-worst terrorist attack in U.S. history, 1995's Oklahoma City bombing, was perpetrated by far-right anti-government fanatics of no particular religious affiliation. The Atlanta Olympic Park bomber (who had previously exploded bombs at women's health clinics and a night club popular with lesbians), identified himself as a Christian and claimed to be motivated by a hatred of socialism and abortion. The 2015 mass murder at the Emmanuel AME Church in Charleston SC was carried out by an emotionally troubled young man reportedly radicalized by white supremacist websites. There have of course been Muslim terrorists as well, such as the person who shot over a hundred people, 49 fatally, at the Pulse gay nightclub in Orlando last June, the single most deadly terrorist attack in the United States since 9-11.
Of course, there are Muslim extremist groups who embrace terrorism as a tactic and have killed large numbers of innocent people especially in the Middle East and parts of Africa. In fact, as M. Steven Fish wrote in his 2011 book from Oxford University Press, the majority of terrorist attacks world-wide in recent years have been carried out by Islamic terrorists. But for Americans and Europeans, he wrote in a more recent article, the risk of being killed by a terrorist in a given year is only about 1 in 3.5 million, and in the United States and Europe Muslim terrorists account for less than half th deaths. In fact, from 2002 on, Americans have faced a greater risk of being killed by their own furniture or television falling on them than of being killed by a terrorist of any description.
Nor, according to Fish, are Muslim societies in general particularly violence-prone.
Homicide rates in Muslim-majority countries average about two murders per annum per 100,000 people. In non-Muslim countries, the average rate is about 8 per 100,000. Murder rates fluctuate from year to year, but they are consistently low in Muslim societies. The homicide rate in Indonesia, the world’s largest Muslim country, is 1 per 100,000 -- one-fifth the rate of the world’s largest Christian country, the United States. Christian countries live with murder rates that are unknown in the Muslim world. Brazilians and Mexicans are used to murder rates in the 15-25 range; the rate in Venezuela tops 50. Turks, Egyptians, Iranians, and Malaysians live with rates in the 2-4 range.
It's also important to recognize that mainstream Muslims condemn terrorism. See this long list of anti-terrorism statements from Muslim leaders compiled by Charles Kurzman, a professor at the University of North Carolina at Chapel Hill (which last night won the NCAA men's basketball tournament, I believe I heard somewhere, but that's another subject).
Kurtzman has extensively studied Islam and Arab culture and has very interesting things to say about Islam and terrorism, for example in this recent article about his work originally from The Deseret News. Kurzman notes that in 2016, the percentage of people killed by Muslim terrorists in the U.S. was smaller than the percentage of Muslims killed in the U.S. for being Muslim. (Both percentages were microscopic.) Even in the Middle East, where terrorist attacks are much more common, terrorist leaders from Osama bin-Laden to Ayman al-Zawahiri have complained about how hard it is to find Muslims willing to join their movements.
A January 30 blog post by Nick Gillespie on the website of libertarian-conservative Reason magazine points out that no Americans -- zero -- have been killed by foreign born refugees in the United States since the Refugee Act of 1980. That's partly because it's so hard to into the country as a refugee. For the most part, the U.S. chooses which refugees to admit rather than refugees picking the U.S. Even the danger of terrorists coming to the U.S. on tourist visas, which are far easier to get, present a very small risk in realistic terms.