Slew Rate Explanation
OK, I'll give it a try.  Inside an op-amp there's a compensation capacitor, typically on the stage after the differential pair.
This capacitor is charged and discharged by a current source.  This current source has a finite amount of current available to charge and discharge the cap.  I.e. it saturates at some maximum current value.
When that saturation happens due to a large fast-changing signal at the input of the amplifier, the amplifier no longer behaves linearly but will &quot;slew&quot; at a rate defined by the compensation cap and the max available charge/discharge current.  dv/dt = I/C.
This means that for example when a large sine wave causes slew rate limitation or distortion, the sine starts to resemble a triangle due to the constant current charging the cap.
Typically, a higher slew rate is better, but if your signals are such that you don't get into slew rate distortion then a less expensive amp might be the better choice.
Here is a good discussion of slew rate.