A mass in 3d space yet, sorry if this so pleb to be ignored.
In classical general relativity, matter is that which has localizable energy, and includes stuff like light and dust, while gravity is the one field that does not have localizable energy. Matter and gravity are postulated to be fundamentally distinct, and gravity does not explain matter.
In Rovellian loop quantum gravity it is postulated that this distinction remains fundamental and so the theory does not seek to explain matter. LQG seems to be roughly ok with matter (spin foams are http://arxiv.org/abs/1103.6264" [Broken] to some sorts of lattice gauge theories), but it may not have gravity.
In string theory it is postulated that both come from a more fundamental thing. String theory seems to have gravity, and is also roughly ok with matter, but we don't know if the matter in the theory matches that of our universe closely enough.
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