What does it actually mean by that a transducer has good dynamic response?
Essentially, it means that it should have a (as most as possible) flat response (sensitivity) throughout the whole bandwidth the entity to be measured is of interest.

Say that you have a microphone, and you want to record music. Usually the audible frequencies span between 20 Hz and 20 kHz (give or take): the best microphone has the same sensitivity through the whole range of frequencies. Instead, if it has a cutoff (say) past 5 kHz, it may attenuate the higher frequencies and filter out the trebles, giving a 'muddier' reproduction of the sound.


  When taken as a function of time


Say that you want to measure your body temperature. You get a thermometer, stick it in your a..rmpit, and wait. After a few seconds, you read the value and that's it. This is a slow transducer, because you don't care about how fast and how the temperature varies, just a mean value.

Instead, if you want to make a virtual reality visor, you need to track the head's movements in order to adjust the image displayed in the screens. You don't just need to measure mean acceleration, you need to accurately track its value over time. By knowing how fast the acceleration can change, you decide how fast the accelerometer (and gyro) needs to be in order to fulfill the requirements.