Newtons Equation for Mechanics
F is the Newtonian force,
a the resulting accelaration,
m the inert mass

Einsteins Field Equations
G is the constant of gravity,
c is the velocity of light, 
R describes the curvature of space time,
g describes the metric of the 4 dimensional space time (metric tensor),
T describes the energy contents of spacetime
R, T and g 
describe tensors, the
indices reference components of the tensors
T is the source of the field of gravity R without indices can be derived from R with indices: sum over the elements of the diagonal   

After Einstein's theory a mass causes a curvature of space time, that means curvatures in space and in time, this curvature results as gravitational force in our three dimensional world of experience.

Mass and energy are equivalent (E = m * c2), the curvature of space time also results if pure energy is localized in a volume of space (i.e if it appears as Photons or pressure). This can be seen if the energy stress tensor is inspected in more detail, the components of  Tik have the dimension of an energy density (see the following site).

The left site of the field equations (curvature and metric) depends from the right site (the energy), but the energy itself depends also from the curvature of space time.

This gives a non linear relationship between energy Tik, metric gik and curvature R, Rik, i.e. resulting in the dynamics of the Universe.

The metric gik in the field equations defines the geodesics of the geometry, this are the "straigth" lines at which free particles move if no outer force acts on them (the gravity is already included in the geometry).

"Geometry tells matter how to move and matter tells geometry how to curve" (Wheeler).