Arrow spine is nothing more complicated than the relative stiffness of the arrow. The arrow stiffness has to be matched to your bow and, in some respects, to your shooting form in order for it to launch properly from the bow.
The spine you need depends on the performance level of the bow, draw weight, length of the arrow, draw length (not always the same as arrow length), and tip weight. The higher the performance level, the stiffer the arrow needs to be. The higher the draw weight, the stiffer the arrow needs to be. The longer the arrow length and/or draw length, the stiffer the arrow needs to be. The heavier the tip you use, the stiffer the arrow needs to be.
And, naturally, the lower the performance level, the lower the draw weight, the shorter the arrow/draw length and the lighter the tip, the less stiff the arrow needs to be.
Arrow weight and spine are not the same thing. Some people wind up confusing the two, looking at the grains per inch. Grains per inch tells you nothing but how much an inch of that particular shaft weighs. Although a stiffer spine arrow shaft does often weigh more than a lower spine, you cannot count on that always being the case. A shaft's weight does not tell you how stiff it is.
Most compounds made since 2000 are warranted to shoot arrows that weigh a minimum of 5 grains per pound of draw weight. A 70 pound bow would be warranted to shoot a 350 grain arrow. 60 pounder would handle a 300 grain arrow. But keep in mind that these are MINIMUM arrow weights to keep your bow in warranty. The warranty should not be taken as a recommended arrow weight.
I will tell you right up front that not everybody agrees with my views on arrow weight. So take any arrow weight recommendation you get - from me or anyone else - with a grain of salt. Or a few tons of it.
The higher you go on performance - the higher energy your bow delivers, in other words - the more you can cheat toward the 5 grains per pound minimum and still achieve adequate penetration on game. The lower you go on the energy scale, the more you have to rely on arrow weight to get the job done.
Personally, I'm a heavy arrow fan and like my hunting arrows to range between 8-11 grains per pound for maximum penetration potential. Some guys shoot 5 grains per pound for everything, because they like speed and the flattest trajectory they can get.
I think a hunter shooting a bow that generates at least 55 ft lbs of energy would choose arrows somewhere in the middle, around 7 grains per pound. A good balance of arrow speed, acceptable trajectory and power. Below that 55 lb threshold, I'd say go up in grains per pound.
I also advocate a minimum arrow weight of 400 grains for hunting. A point of view a great number of people disagree with to the point of apoplexy.
There is a good site run by Steve Jackson where you can get a whole bunch of good information. Arrow spine charts, weight/FOC calculators, ballistics calculators, etc. Some of the sections could use some updating, but it's still an excellent resource.
http://home.att.net/~sajackson/archery.html