RC Low pass EMI filter for IN-Amp, component specification
What would happen if you want to measure a 1 MHz signal but the bandwidth of your measurement amplifier is also 1 MHz ? At that frequency your input signal will be attenuated by 3 dB. This is because the definition of bandwidth is the frequency point where the attenuation is 3 dB. So your measured signal would be smaller than the actual signal at Vin.

Now what would happen if you want to measure a 1 MHz signal but the bandwidth of your measurement amplifier is much more, it is now 100 MHz. There would hardly be any attenuation of the signal.

The 100 times more bandwidth will result in a considerable margin regarding attenuation caused by a limited bandwith. If you do not require large accuracy then 10 times more bandwidth could suffice as well.