Static spine is the measure of arrow stiffness at rest. Typically, the static spine is measured by resting an arrow on two narrow points either 26 inches apart or 28 inches apart. A weight of a certain size (2 pounds I believe) is hung from the center of the arrow shaft, and the deflection of the arrow (think sagging) from horizontal is the measure of static spine. Downward pressure using a gauge (spine tester) can be used instead of hanging a weight.
Dynamic spine is a measure of how much the arrow flexes when fired. Things like smoothness of release, how tight a nock clamps to the string, draw weight, draw length, string material (dacron versus fastflight) all may or will have some impact on how much the arrow flexes.