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The pinnacle of the theory is equation~\ref{einstein}, which is actually a set of 10 equations called {\bf Einstein's Field Equations}.   These equations describe gravitation as a result of space-time being curved by matter and energy.   Space and time are described through can be measured using  the so-called metric tensor (a tensor is a mathematical object analogous to but more general than a vector), which enters through the quantity $G_{\mu\nu}$. The metric tensor allows to measure space and time. But equation states that  the result of the measure does not only depends on space time itself, itself  as expected in Newtonian mechanics: Mass and energy appear in Equation ~\ref{einstein} via the quantity $T_{\mu\nu}$, also called the stress-energy tensor. The stress-energy tensor basically measures the density and flux of energy and momentum. So curvature is zero only where there is no mass and energy. As soon as mass and energy are present, space and time are affected. The orbit of the Earth around the Sun is explained by the curved space-time produced by the large mass of our star. The resulting orbital motion of our planet simply results from the change in the metric, in accordance with Einstein's Field Equations. Gravity is not a force that is added on top of space-time. Gravity is just an emerging property of space-time.