Compliance basically is reversed (spring) stiffness, i.e. displacement per force instead of force per displacement. Typical range for hifi cartridges is about 10 to 50 µm/mN - but of course one could also write that as mm/N or m/kN, which would be easy conversions (numerator / 1000 and denominator / 1000 each, so we can scratch/reduce that). However, you could also convert to less easily applicable unit variants - like for example cm/N, so that we'd need an additional
"x 10^-1" as correction factor, if we'd still like to state that same range as 10 to 50 (x 10^-1 cm/N). Well, and the dyne is a pretty small unit of force (1 N = 100000 dyn) - so if we'd start at our equivalent 10 to 50 mm/N, we'd need numerator / 10 and denominator x 10^5 = numerator x 10^-6 to arrive at our desired 10 to 50 x 10^-6 cm/dyn.
So that's merely a bit of conversion math in order to present nicely readable values. And because both of the usual styles, yy µm/mN and yy x 10^-6 cm/dyn, describe just the same range, the lazier among us phono fans have adpoted the "cu" for "compliance unit(s)" as conveniently typable "replacement (pseudo-)unit".
Well, and both (or maybe even all three, if we regard Japan style dynamic compliance @ 100 Hz as somewhat different matter compared to dynamic compliance @ 10 Hz) types of compliances can be useful. The type of compliance you need for working with the usual
tonearm resonance formula is the dynamic compliance at 10 Hz, though.
Greetings from Munich!
Manfred