Can somebody explain the Warp Theory Equation?

Could somebody please explain the following equation for me?
ds^2 = −c^2 dt^2 + [dx − vs (t)f(rs)dt]^2 + dy^2 + dz^2 where f(rs)=(tanh(σ(rs + R)) − tanh(σ(rs − R)))/(2tanh(σR).

I've wrestled with it for a while, but quite frankly do not get it. I'm only up through Calc II, but I'm more than happy to learn a few new concepts, should the need arise. This uses the familiar coordinates, (t, x, y, z) and curve x = xs(t), y = 0, z=0 where x is analogous to what is commonly referred to as a spacecraft’s trajectory.