Frequency division detectors work by amplifying the signal from the bat, then frequency dividing it with a digital IC. The amplitude (loudness) of the signal is lost in this process, and the result is a crackly sound, as you can hear in this example.

Each time the incoming signal passes through zero a one is added to a
counter. When the counter reaches a predetermined value (normally 16 or 32) the
output signal changes, as shown here. This means that a bat call at 48kHz (maybe
from a pipistrelle) will cause an output signal at 48/16 = 3kHz.
This output signal is easily audible.
A frequency division detector will allow you to listen for all
types of bat at the same time. It doesnt need tuning in to a particular bat
species. The ability to cover the whole bat spectrum is most useful if your detector
has a good (expensive and fragile) sensor. Cheaper detectors that use miniature
electret hearing aid microphones, or worse still piezodetectors, would not
greatly benefit from this approach.
More expensive detectors such as the BatBox Duet use the frequency division with amplitude restore principle to put
back the lost loudness information. (see below) These also use capacitance microphones that are
expensive and fragile and also not very sensitive!

The output from frequency division detectors can be recorded for later spectral analysis, which is not a possibility with heterodyne detectors as with these the frequency content is changed by an unknown amount. By contrast in f-div detectors the incoming frequency is scaled by a known factor - often 16 or 32.
New developments: amplitude restoration
Some frequency division detectors overcome the problem of lost amplitude information by detecting the incoming amplitude, and restoring it in the output signal. This provides even more information for analysis, and a nicer sound.