Ever had to answer that question? I have. There's not a perfect answer, but here's where I net out:
Caring is an easy way to measure the amount of passion that someone feels for something. For example, the guy at the fast food restaurant that slops stuff together and delivers it to you cold and without a smile -- he doesn't have much passion for his job. Compare that to the guy at the suit department at Nordstrom that follows up with a phone call and personal letter after every single purchase, and that calls to check in occasionally when he sees something you might like -- tons of passion for his job.
It's easy not to be passionate about things; being passionate takes work and commitment -- caring takes work and commitment. I find that it's very easy to by passionate (and to care about) things that you love, which is why I always encourage anyone that cares to ask to do things that they love, to spend time with people that they love.
What does passion (and, for that matter, caring) really net out to be? Emotional commitment. Here's one of my favorite quotes from Tom Peters regarding emotional commitment: "People can smell emotional commitment (and absence thereof) from a mile away." (note that this is as important in your business life as it is in your personal life).
Emotional commitment = passion = caring
Ansel Adams picture from pingnews.com