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

[Jackalope]

Been hearing all my life from Christians that "we have a hole inside of us that only god can fill, and we may try to fill it with girls, video games and foods but only god can fill it" :S

and even some non christian people talk about "feeling empty inside".

what does it mean to you?

I believe that what people generally mean by such statements is "Without X, I see no purpose or reason to it all".

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It's basically the same thing as existential angst.

Yes, this. That's the phrase I was grasping for and not finding.

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From a existentialist point of view, foregoing belief in God comes at great cost.

Except it doesn't, not necessarily. The cost for me has been "If I feel a need for meaning and purpose, I must find my own."

In the absence of God the universe is absurd

That would be from an absurdist point of view, not existentialist.

life becomes an empty gesture

That would be from a nihilist point of view, not existentialist.

I think I see what you're getting at here, but it appears that you're conflating some heavily nuanced terms.