What does it mean to have a "Roman Catholic" affiliation?

I know that some colleges and universities are very lenient when it comes to religion, but I also know others are very strong in their religious beliefs and require you to take religion courses. I plan on applying for Seattle University and in the description it said it had a "Roman Catholic" affiliation. What exactly does that mean? Would I have to take a religious course? Are they strict? I'm not Catholic, will I have a lesser chance of getting in?