We often say flex or flexural modes, with the same meaning as Mike.
What we actually mean is that the steel is bending, rather than the component bouncing or whatever as a rigid body on its isolators.
Subframes, cradles and cross members need to be stiff because they are terminating isolators, if they have resonances in the range of excitation seen then they will have a reduced impedance, and so more noise and/or vibration will be felt by the car's occupants.
Japanese car companies often seem to specify minimum modal frequencies for subframes and so on in free-free conditions. I don't think this is very helpful, and would much rather look at the mobility of each isolator mounting point, as installed in the vehicle. The sad truth is that many subframes are stiffened by the body, even though they are supposed to be isolated! This doesn't happen so much these days, fortunately.
Cheers
Greg Locock