Spine is basically the amount an arrow shaft is able to bend; in general, heavier poundage bows require stiffer spined arrows. The reason a heavier tip requires a heavier spine is inertia; it takes more input to get the heavier head moving. Therefore, given the same spined shaft, a heavier head is going to cause the shaft to deflect (bend) more than a lighter head would when the shot goes off. (Think of pushing a 10 # block with a bamboo pole compared to how much that pole will bend if you push a 50# block with it.) There is a certain amount of arrow deflection that is needed for each set-up so varying the spine rating of the arrow with regard to poundage, shaft length and tip weight is how that deflection is obtained, some other factors that play into determining the spine of an arrow for a certain bow set-up are: cam design (energy transfer), release or fingers (torque imparted), and whether it's a traditional bow where the arrow has to bend around the riser or a shoot through style like most modern compounds.

All arrow manufacturers have spine charts that take most of these factors into consideration when recommending an arrow for your bow.