Compliance has to do with the suspension of the cartridge. Think of the "compliance" of the cartridge as how stiff or "cushioned" the ride is in your car. Some transfer every bump in the road back to you while others let them go un-noticed.
All cartridges have varying compliance / "stiffness" in the suspension that holds the cantilever. The cantilever is the rod that the stylus ( diamond needle ) is attached to. In turn, the cantilever is loosely anchored near it's mid section but also attached to more parts up inside the cartridge body.
Depending on the type of cartridge, it could be connected to small but very powerful magnets ( moving magnet )that are placed within the field of two different coils ( one left, one right for stereo ). You can also take the opposite approach and have the coils attached to the cantilever and keep the magnets stationary ( moving coil ). Each design has it's own benefits and drawbacks with output levels being one of the major differences.
There are other exotic designs out there but the one that you might run across that i didn't mention was Moving Iron ( MI ). It is similar in principle and output level to the Moving Magnet but slightly different. I won't go into the differences amongst the various types as each design and the type of materials used can be extremely varied. Trying to lump one design as being better / worse than the other would surely be doing a dis-service to the stand-outs of each type.
Anyhow, the stiffness ( or compliance ) of the cartridge suspension will vary as to how much motion is absorbed or transferred back into the arm from the vinyl. Since a lighter arm has less mass, it can be moved around more easily. You would therefore have to be careful as to the type of cartridge that you mated it with. A suspension that transferred a lot of energy ( rather than absorbed a lot of energy ) back into the arm could cause "mistracking". Mistracking occurs when the cartridge can't stay centered in the groove due to a lack of downward applied force or improper alignment.
In this case, we'll assume that the cartridge is properly aligned but the arm / cartridge selection was incorrect. Once the cartridge transferred a "big" warp or extremely loud passage (like the recording of a cannon blast on the 1812 Overture) back into the arm , the arm may be too light to damp or absorb the energy. As such, the arm literally sees that big transfer of energy from the cartridge as a momentary "kick". If it is a hard enough kick, it will minimize downward force enough to allow the cartridge to mistrack. In severe cases, the cartridge will literally jump completely out of the groove. Needless to say, this isn't good for the vinyl or the cartridge.
As you might have guessed, i've tried to keep this simple. I tried to do that for two reasons.
1) So that those that are just getting started ( or re-started ) in vinyl can follow along and pick up a very basic understanding of what is involved in selecting compatible components
2) So that i didn't make a fool of myself or spread "misinformation". This type of stuff can become very complex. I will be the first to say that i know just enough to be dangerous when it comes to vinyl.
With that in mind, i do know that Albert is a very experienced and helpful kind of guy when it comes to vinyl. Maybe he'll jump in here or as he sees fit to help some of you folks out.
In the meantime, try picking up the following "pamphlet" about what is involved in setting up a TT / vinyl rig. It covers a LOT of basic info and is pretty easy to follow along with. It is available from the following website that is owned and operated by George Merrill:
You are looking for "How to set up and tune your turntable and tonearm". I think it ran about $8 - $10 or so. George Merrill is a well respected "vinyl-head", so you can pretty much believe what you read without a lot of controversy involved.
You might also want to look for a book called "Good Sound" by Laura Dearborn. This can probably be found at Amazon or through your local library.
Hope this helps. If i have stated something incorrectly or made things confusing for some, PLEASE correct / clarify my mistakes for me. I'll be glad to learn anything that i can on the subject. Sean