Please follow the link below. It should answer most if not all your questions.
Some additional links to good information that will help you get oriented:
The Audio Asylum FAQ, with many additional links:
Laura Dearborn's excellent discussion of turntable setup:
Retail sites, but with good information and diagrams:
A phono cartridge is a transducer - just like a loudspeaker, but in reverse - it takes mechanical motion and transforms it into an electrical signal. The motion comes from the stylus wiggling in the vinyl groove. This intern moves a coil inside the cartridge next to a magnet, producing a tiny electrical signal (or moves a magnet next to a coil inside the cartridge, with the same result).
Because you want only the motion of the stylus in the groove, and no other motion, to be converted into the signal, the relationship of the cartridge to the arm - particularly their relative masses but also the arm's form of pivot, and its isolation from outside vibrations, are crucial. So is the alignment of the arm and stylus in relationship to the vinyl groove, which must be precise.
Perhaps the key issue in cartridge-arm matching is the weight and compliance of the cartridge, on the one hand, compared to the weight and structure of the arm. You don't want the stylus feeding back extra energy into an arm that can't handle it properly, thus creating an audible resonance in the signal.
To quote an ancient post from somewhere (I copied this ages ago - my apologies to the original poster, whose name I have lost):
"A LOW-TO-MODERATE compliance design has a relatively stiff stylus cantilever suspension in the 8-15cu range.
"The MEDIUM compliance range runs approximately from 15 to 25cu.
"Very softly suspended cantilevers fit in the HIGH compliance range, from 25 to 50cu."
Arm/cartridge resonance should be in the 8-12 Hz range. This then brings us to the arm weight. Effective mass of 5-7g would require 25-50cu compliance from the cart to achieve 11 Hz resonance. The calculation is:
Hz = 1000 / 2 x Pi x sqrt (MC) where
Pi = 3.14159
sqrt = square root
C = stylus compliance
M = effective mass of arm PLUS cartridge, in grams
There are many Excel spreadsheets floating around the web with this calculation, or you can try entering it yourself.
Another issue that has arisen on this board but isn't addressed by this formula is the form of pivot used by the arm. Dual or gimbal pivots are more inherently stable than so-called unipivots (where the arm floats essentially on an upward facing pin), and therefore can handle the feedback from a low-compliance cartridge better. If the unipivot has a fluid damping trough and/or outriggers it may be able to handle low-compliance cartridges with greater aplomb.
Of course, this is just one part of the analog equation. System synergy is important too. A given arm may be more comfortable on a non-suspended turntable than a suspended one, for example.