"compliance" just means by how much a spring complies under load. The stylus assembly on the cantilever and suspension is regarded as a spring and the load is the mass of the cartridge + the VTF. The units are basically distance per force in 1 millionth (10 in the power of -6) of a centimeter per dyne. It can also be expressed as meters per newtons but we don't really care. We just call it "cu" for compliance units. It's kind of like a currency where 20 cents is always less than 30 cents so 20cu is always stiffer (less compliant) than 30cu. The difference is we have two different currencies with a funky and volatile exchange rate. More about that in a bit...
Static compliance is like measuring the compression of a spring with some load (weight) applied to it. More weight, more compression - it's a linear straight forward relationship. Not many manufacturer's exclusively settle for the static compliance of their carts.
Shure is a notable exception. I don't know why they only state static compliance but it's a source for confusion and misconception regarding their carts compliance. It's not a common practice and definitely not very informative. It is, however,
static - hence frequency independent.
Dynamic compliance is a little more complex b/c if you take the spring and oscillate it 10 or 100 times per second, (cycles per second, or simply "Hertz" or "Hz" units), and try to measure the distance it compresses with the same load as before, it would be very different. Not only that, it would also vary between the 10Hz and the 100Hz.
With the analogy of the cantilever and a loaded spring, the frequency at which dynamic compliance is measured becomes important. The cantilever actually oscillates all the time as a reaction to the stylus reading the groove modulations. Static compliance isn't exactly the best indicator of performance in this case. Most manufacturers specify dynamic compliance and sometimes provide the static compliance too - but they do not all use the same frequency in dynamic compliance measurements!
Here's where we use two different "currencies". The Japanese traditionally measure dynamic compliance at 100Hz, while the rest of the world uses 10Hz. Everyone calls it "cu", just like many currencies use "cents" to denote the 1/100th part of the whole. For dynamic compliance the frequency is critical - just like knowing the currency of a price denoted in cents. Is it Euro cents or USD cents? It matters - a lot!
Unfortunately, there's no good equivalent of a currency exchange rate between cu@100Hz and cu@10Hz. A Denon DL-103 dynamic cart compliance is specified as 5 × 10 - 6 cm/dyne (100 Hz) and conforms to the Japanese standard of denoting it. To convert it to 'our currency' of cu@10Hz, we generally use a multiplier of anything between 1.5 and 2.2 and we try to factor in the mfgr recommended VTF, under the assumption that higher VTF goes hand in hand with the less compliant carts. I like to use 2.0 so the Denon 103 compliance at 10Hz is 5 X 2.0 = 10. It's arbitrary, inaccurate and unfortunately doesn't work very well in all cases. Some Nagaoka carts turn out to be way more compliant than this method indicates.
Finally - the point of knowing the cart's compliance in cu@10Hz terms becomes important in regards to calculating the resonant frequency (RF). RF is the frequency that may induce the cantilever to oscillate in an ever cascading uncontrollable manner. It's bad thing for us but it's a physical thing that will happen to a loaded spring and we can't avoid it. We can, however, try to restrict the spectrum of frequencies at which this happens to a known 'harmless' range.
Our ability to control the RF depends on the relationship of the cantilever compliance and the effective mass of the tonearm. Effective mass is not in any way the weight of the tonearm - or it's mass. It's a layman's term which describes the tonearm's total moment of inertia and it roughly equates to a car's road handling as a function of it's mass distribution over it's dimensions and it's suspension system.
In a nutshell - the tonearm's inertia is a force that opposes the stylus desire to change direction as a reaction to the groove's modulations. We want to keep this conflict at minimum for as much as possible. The general rule to approach the equilibrium in this domain is low compliance ('stiff') carts are compatible with high effective mass tonearms (hefty) and high compliance carts ('springy') match low effective mass tonearms (light). We need the cu@10Hz b/c most cart/tonearm matching formulas rely on the compliance at 10Hz. See
more about cart/tonearm compatibility here.
I hope this makes sense. I've tried to be brief but it's a rather encompassing subject so I guess that's as short as I could make it.
TL;DR I know I did not give you the range split in cu for low, medium and high compliance, but that's just because it's as volatile, arbitrary and varies as much as who you ask.
Be your own judge.