Adjusting the bandwidth of a sensor

Hi

What means the bandwidth of a sensor?

According to datasheet of some sensors (such as accelerometers) we can adjust the bandwidth of sensor with an external capacitor. What trade offs are involved in adjusting bandwidth?

thanks

check these basics
Understanding Sensor Resolution Specifications and Effects on Performance

In a real-world data acquisition experiment, the physical phenomena you are measuring has expected limits.
For example, the temperature of your automobile's cooling system varies continuously between its low limit and high limit.
The temperature limits, as well as how rapidly the temperature varies between the limits, depends on several factors
including your driving habits, the weather, and the condition of the cooling system.
The expected limits might be readily approximated, but there are an infinite number of possible temperatures that you can measure at a given time.
As explained in Quantization, these unlimited possibilities are mapped to a finite set of values by your data acquisition hardware.

The bandwidth is given by the range of frequencies present in the signal being measured.
You can also think of bandwidth as being related to the rate of change of the signal.
A slowly varying signal has a low bandwidth, while a rapidly varying signal has a high bandwidth.
To properly measure the physical phenomena of interest, the sensor bandwidth must be compatible with the measurement bandwidth.

You might want to use sensors with the widest possible bandwidth when making any physical measurement.
This is the one way to ensure that the basic measurement system is capable of responding linearly over the full range of interest.
However, the wider the bandwidth of the sensor, the more you must be concerned with eliminating sensor response to unwanted frequency components.