Hi OakIris,
Cartridge compliance is the stiffness of the suspension donut that holds the cantilever assembly in the body of the cartridge. It is the thing that allows the coils to be moved inside the magnetic field inside the cartridge. The compliance of cartridges is rated in units of CU(compliance units), with low compliance being generally considered under 10cu, medium-low compliance typically from 10cu-12cu, medium compliance from 13cu to about 20cu, medium high compliance from 21cu to about 25cu, and high compliance anything over 25cu. These are general ranges and some people may quibble about details, but they are pretty close to being what is generally accepted. Low compliance cartridges have stiffer suspensions, and high compliance cartridges have very soft suspensions, and the spring force of these suspensions has an effect on the interface of the cartridge and the tonearm.
With regard to cartridge/tonearm matching, the rule-of-thumb is that as the compliance gets lower, the effective mass of the arm must increase, in order to have the ability to keep the cartridge stabilized over the groove, and also to make a happy mass/resonance frequency in the desired range of 8Hz-12Hz. Going lower than 8Hz in mass/resonance can cause the system to be excited by rumble frequencies which is not desireable, and going higher than 12Hz can cause the resonance of the arm/cartridge matchup to have an audible effect in the audio range above 20Hz. So, when we look for matching arms and cartridges, we strive to have the mass/resonance match within this range mentioned above. Sometimes the match can yield somewhat higher than desired results, and still sound quite good. But we want to get as close as possible to the desired range.
There are charts available on the web which have matching curves for choosing cartridges which match to certain effective masses of tonearms, but these are general, and don't include all of the information needed for complete matching criteria, but they are a good general guide. You can also use the HFN&RR test record to check the exact resonance in your system.
What they don't tell you is that there is significant energy fed back into the tonearm and bearings, which can cause the tonearm to move in unwanted ways, or make the bearings chatter or break down. This energy is most severe in low compliance cartridges, and this is why I use and recommend quality higher mass gimbal-bearing tonearms for low compliance cartridges. Unipivots can be used on low compliance if there is a specific method of stabilization present on a unipivot tonearm, and if they have the correct mass needed for it.
So, for high compliance cartridges, generally you look for a lower mass(less than 9grams) tonearm to match it. For medium compliance cartridges, you look for a medium mass(9g-11.5g) tonearm to match. And for low compliance cartridges, you look for a high mass arm of over 12grams(and sometimes much higher, depending on how low the compliance is). The high mass arms and low compliance cartridges seem to be the most difficult matches to make because there is so much energy being sent back into the arm to excite everything, that much more than just the mass/resonance issue comes into play. Generally, it is less risky for beginners to start out with something in the medium mass/medium compliance range, because they are less likely to make a big mistake there. But, there are great sonic rewards in the low compliance cartridges, if you make a good match for them.
Typically, I make my matches by the "seat of my pants" because I've had a lot of experiences with many different matchups. But, a beginner should learn the basics first, and then try to fly later.
You can do some Google searches on the key words I've used and you'll come up with a variety of articles with charts and graphs to help you.
And, if you are in a quandary, just email me and I'll help you out.
BTW, the HiFi mod makes the effective horizontal mass of the Rega arms and OL Silver arms high enought to stabilize the low compliance cartridges, even though the effective mass of the standard tonearm is marginally too low for the use of such cartridges. The result is that the shortcomings of the matchup are overcome by the use of the HiFi mod.