It can measure the static acceleration of gravity in tilt-sensing applications, as well as dynamic acceleration resulting from motion, shock, or vibration.
So, yes, measuring vibration is possible.
The user selects the bandwidth of the accelerometer using the CX, CY, and CZ capacitors at the XOUT, YOUT, and ZOUT pins.
So, one would suppose then that the different steady-state readings reflect different capacitors for the different axes.
Posting a link to the particular device you have might be a good idea.