Civil liberties are those rights that we all have as individual Americans. These can be contrasted with civil rights, which are the sorts of rights that are associated with groups. Therefore, laws preventing discrimination against African Americans are civil rights laws. By contrast, the First Amendment, the Fourth Amendment, and others are examples of civil liberties. Civil liberties are things like the freedom of speech and religion.
The main implication of civil liberties is that they make us a free nation. The fact that we have civil liberties is what makes us truly democratic. In countries without civil liberties, people may not, for example, be free to criticize the government. Any country in which people cannot criticize the government cannot possibly be seen as a true democracy.
Another implication of civil liberties is that we are a pluralistic nation. We have freedom of religion and therefore we can have many different religions (and people with no religion) as part of our society. This makes us very different from more homogeneous countries that have fewer civil liberties.