A metaphysical claim is one that can not be proven scientifically because it is outside the realm of scientific experiments. I think these claims are important because I don't think we should know everything, I think there still has to be some parts of our world that we don't understand. I'm not saying I agree with every single metaphysical claim there is, but I think that it's important they are there.
In my life, a good example of a metaphysical claim is astrology. Personally, I believe in astrology because the information it has given about me and who I will be has lined up exactly with my character. However, the scientific part of me knows I probably shouldn't believe in it, because how can astrology actually be proven? I think this article does a good job of going over astrology and what it qualifies as; http://atheism.about.com/library/FAQs/skepticism/blfaq_astro_sci_pseudo.htm
In the media, astrology is commonly used. For example, you can always find horoscopes in newspapers and magazines. For example this website offers horoscopes every day: http://my.horoscope.com/astrology/free-daily-horoscope-pisces.html
1. Ruling out Rival Hypotheses: Horoscopes and astrology tell you certain things are just going to happen, but that really isn't true. People have the ability to make their own choices and decide where they want their life to go.
2. Correlation vs. Causation: A horoscope may claim that you are going to have a horrible day and you actually do end up having a horrible day. You therefore decide it's because of what sign you are, when in reality it's other things going on in your life.
3. Falsifiability: A study can't really be designed to test astrology.
4. Replicability: Horoscopes and astrology may claim to be accurate, but that isn't true. What horoscopes say are going to happen can't happen to every single person of that sign.
In reality I don't think horoscopes are anything to really be paid attention to, because events in our lives occur because of chance and what we ourselves do. In spite of this, there is still that part of me that believes in astrology and I know this is true of many others. I wonder why we do this? What is it about astrology that makes me and others believe parts of it are true?