What does it mean that Einstein's equations are hyperbolic-elliptical?

I says on Wolfram MathWorld that Einstein's field equations are a set of "16 coupled hyperbolic-elliptic nonlinear partial differential equations".

What does it mean that the equations are hyperbolic-elliptical?

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It means solving them is hard. And what Jerry said. –  Chris White Feb 14 '13 at 21:52
Well, the coupled-nonlinear part makes them hard. Solving the wave equation is easy. –  Jerry Schirmer Feb 14 '13 at 22:05

The basic example of an elliptical set of equations would be Poisson's equation--here, you don't evolve in time, so you don't specify an initial time value to evolve the equation. Rather, you specify the value of the function on some boundary, and then you integrate out/in from that boundary using the equation to find the values elsewhere. In the most basic case, think about when you chose a surface where $V=0$ when you were solving electrostatics problems. This often arises when solving for constraints in dynamical system.