Are you having trouble with the vocabulary, or simply the layout of the sentence? Since I'm trying not to doublepost, I'll give you some of the harder vocabularly, and then we'll analyze the sentence from there.
immigrant-someone who is not from the nation (in this case, the US)
globalization-the interaction of countries between each other. This results in shared ideas, cultures, languages, foods, etc.
phenomenon-something that takes place (this one is a little bit harder to define)
migration-the movement of people from one place to another
policy-a practice (for example, a law or something that is followed)
So in this case, this is more or less what the sentence is saying:
Today America is being challenged by the wave of new immigrants coming in the country. Because of the spread of ideas and cultures, the movement of people and the violent acts of terrorism have become easier. Although Americans are used to accepting these new people and their cultures as harmless, this is no longer possible.