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They call it the "fabric of reality" because that's a good metaphor to describe how gravity works. (Or at least I assume that's where it came from, I could very well be wrong.)
When you stretch a fabric thin, and place something heavy in it, it's going to sink and stretch the fabric down with it. Then, if you place a smaller object next to the larger one, it's going to roll around the larger one, gradually moving closer as it goes down the slope created by the larger object.
That might be hard to visualize, so here's a neat video I found.
Edit: guys I think you're reading too much into this I wasn't trying to provide a foolproof explanation of how gravity works I was just trying to relate an interesting metaphor to a piece of linguistics.
And I wasn't even right, a quick google search says the term predates our understanding of the universe. Its probably a coincidence.
I think that explains the "how" more than the "why".
What I meant was that's "why" we use the term "fabric of reality"— because of "how" gravity works.
Indeed, it's a neat way to visualize gravity, but that's it. It lacks any sort of explanation of why masses appear to be pulled towards one another. (I will point to the other person in this thread saying it "explains gravity with gravity".) This is why I think the metaphor you mentioned detracts from the original video.