The FBX exporter bakes animations at the given sampling rate. Basically you get one keyframe for every frame. Of course if the original curve wasn't changing over a particular range of time, baking gets you a bunch of duplicate keyframes. "Simplify" cleans these up by deleting keyframes that differ very little from the last keyframe. This saves space in the FBX file.
The simplify option is a factor that controls how much two keyframes are allowed to differ before they are considered different for the purpose of "simplify". With the default factor of 1.0, this is a relative difference of 0.01% or (for numbers close to zero) an absolute difference of 0.0001.
The relevant function to read is
I'd leave it as the default value, but you can see if using 0.0 will fix it if you have some kind of problem with animations.