The biggest threat to the safety and freedom of those living in the West today is an extreme form of Islam called Islamism. The ambition of its votaries is to impose strict Islamic law, sharia, on the entire world, including Europe and the United States.
These fanatics realize that they can't persuade Westerners to adopt Islam and sharia through the free exchange of ideas and rational argument because their religion, based as it is on a strict fundamentalist totalitarianism, has very little appeal to people who are accustomed to the freedoms enjoyed in the West for the last two and a half centuries.
Their hope, therefore, is that by overwhelming democratic states with refugees and other immigrants who will eventually be given the right to vote they can gradually acquire sufficient political power to enact the strictures of sharia legislatively.
If and when they succeed the very freedom they exploited to gain their ends will be abolished and people will one day awaken to find themselves under the thumb of an alien theocracy with the power to dictate every aspect of their lives and to compel everyone to conform to the teachings of the Koran on pain of death.
Meanwhile, the Islamists know that in the postmodern West the highest values of millions of people are mere peace and security. Believing in little else, these people would rather submit to the dominance of the Islamists than live in constant fear. Thus, the will to resist the capitulation of the West to the Islamo-fascists is being steadily eroded, especially in Europe, by acts of terror committed by Islamists willing to die in order to sap whatever confidence remains among Westerners in their values and institutions.
We're often told that terrorists are a small number of those who adhere to Islam, and in relative terms that's probably true, but in absolute terms they number in the millions.
Prager U. has a helpful primer on Islamism which packs a lot of facts into a five minute video. Give it a look: