what do christians (and people in general) mean by "feeling empty inside"?

[Neo-Scholastic]

I found that my current life had much more meaning when I realized that there was nothing beyond it. That, and the realization that my life was my own to manage, gives me a feeling of freedom and power and the motivation to enjoy the life I have even more than I did before.

I had the same experience as an atheist*. One of the most attractive things about Existentialism is the sense of taking full responsibility for your own life. Taking God out of the picture removes one more external constraint on a young man's life and a source of much hand-wringing like "did I do the right thing". Of course it doesn't mean you go balls out Dostoevsky. You still have your old habits. If you're kind and like to fly kites as a Christian, you'll probably still continue to be kind and fly kites. Personally, I did not change how I lived much at all. Even if life had no ultimate meaning, I could assign it proximate meaning for the duration of my life.

It took me a while to realize that I had lost something of value. Generally I think the basics of physical life are pretty simple...Eat, Drink, Man, Woman. To me it seems that life, as in Life, goes beyond meeting our purely physical needs. We have an inner life. We love and we think. These two things, loving and thinking, make us human and are what give life meaning and purpose.

So being a naturally reflective person I continued to contemplate things like the Good, Truth, and Beauty. Finding support for these trans-personal values, the ones that make life come alive, is not easy when you're committed to physical reduction. Like the professor in Crimes & Misdemeanors said, "The universe is a pretty cold place." And so it was the more I filtered reality through that lens that everything is quantifiable. When you start to think that the qualitative aspects of life are not real or important, you start to lose (at least I did) slowly and inexorably the sense that life has any value at all.

* The fact that I once was an atheist and am no longer one is not meant to be patronizing. It is just my personal history and places my comment in context.