Physics theories are made by building mathematical models that correspond to physical systems. General relativity, the physical theory of gravitation, models spacetime in a geometrical way: as a 4D manifold. The concept of manifold is just a generalization to the multidimensional case of the usual concept of a 2D surface. This will allow us to apply the well-known tools of differential geometry, the branch of mathematics which describes surfaces, to the study of spacetime geometry.
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Bona, C., Bona-Casas, C., Palenzuela-Luque, C. (2009). The 4D Spacetime. In: Elements of Numerical Relativity and Relativistic Hydrodynamics. Lecture Notes in Physics, vol 783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01164-1_1
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