This is how I understand
Kaluza-Klein theory: General Relativity directly explains gravitational deflection of light, and describes but does not explain gravitational acceleration of matter. Kaluza's insight was that if light propagated in a compacted fourth spatial dimension, its gravitational deflection explained by GR would look exactly like gravitational acceleration of matter in the 3 ordinary spatial dimensions -- so maybe matter is actually electromagnetic energy propagating in a compacted fourth dimension.
If the above explanation has aspects that are correct, I hope that a real physicist can add the information to the article.
Upon further reading, I see that Kaluza's original idea really attempted to unify gravity and electromagnetism in a single geometric theory. That is a really useful thing to do if the result explains things like the equivalence of gravitational mass and inertial mass, or how an electron absorbs or emits a photon.
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