What does the curvature of space-time represent?

If it represents gravity then it is only representing a 2d model of gravity.

A higher degree of curvature represents a greater amount of gravity?

I am asking because in a more complex model of gravity you need to take into account the curvature of space-time above and below the gravitational plane.
This is giving me problems because in a 2d model the curvature seems to be a fuction of the distance from the center of the gravitational plane, in a more complex model you need to represent the curvature at a distance perpendicular to the gravitational plane. The function for curvature over distance is no longer valid as the curvature tends to decrease with an increase in perpendicular distance for any fixed distance from the center in the gravitational plane.
It's like having 2 circles with the same radius but having different cuvatures.
Can curvature have 2 properties, what would they be?

The rubber sheet,2d analogy is just that, an analogy. Space-time is a 4 dimensional vactor space, and unless you can visualise 4 dimensions(which no one can), then you are confined to construct at most 3d analogies.

Simplistically, curvature is the gradient of space-time.