Stress Curve Overview
A taper is what defines a rod's action. Action is the way in which a rod flexes during casting. By modifying the diameter of a rod throughout its length, one can make rods with massively varying degrees of actions.

Tapers are designed in many ways. Trial and error are always the final factors in determining whether a rod is 'good' or not, but there are other ways of creating and modifying tapers.

Everett Garrison, being an engineer, created a way to look at bamboo rod tapers by graphing the static stress at each point along a rod's length. The stress values of a rod are computed by taking many variables into account including the weight of the bamboo, finish, guides, ferrules, etc. plus the diameter of the rod along points along its length. From the resulting stress curve charts, it is fairly easy to visualize the action of a rod using strictly the taper measurements.

Stress curve charts, or simply stress curves, are graphed as follows. A rod's tip is represented on the left side of the graph along the X axis, and the butt section is on the right. The Y axis contains the computed stress along each point of the rod. Basically, the higher the point, the softer, or more flexible, it is at that point on the rod.
To the right is a stress curve chart for a Powell B8.7 straight taper - one whose diameter changes a uniform amount of .0145" for each 5" along its length and whose tip dimension is .070"
Compound tapers are ones that are not straight tapers, or tapers that get slightly wider or more thin at various points along the length. Almost all bamboo rods are built off of compound tapers. As an example, a fast action rod is one that has a relatively soft tip and a stiffer butt section, where most of the rods flex is in the uppermost section(s) of the rod. A faster action bamboo rod stress curve chart will often look something like the graph for a Dickerson 8013 to the left.
A 'parabolic' rod is one that has a stiffer mid section pushed by a relatively softer butt.  The tip can be anywhere from really stiff to quite soft. The ubiquitous Paul Young Para 15 is an excellent example of this type of action.
To the left is another rod action that is called 'parabolic'. The shared characteristic with the Young parabolic rod above is obviously the relatively soft butt section and stiffer mid. However, this Pezon et Michel Ritz Fario taper lacks any softening in the tip section. This basic curve shape is also seen in the few Payne parabolic rods that exist. To me, and in keeping with the general patterns of stress curves, this shape would be better described as 'slow' action.
Though 'slow' is often used as an equivalent to 'soft' the Orvis 7' 3 weight stress curve to the right is probably a better example of a slow rod:  One with a very soft, flexible mid section that doesn't show the characteristic soft butt of a parabolic. 
Garrison used his stress curve charts to create wonderful medium, or progressive action rods. Garrison found that tapers with smooth, horizontal stress curves generated this type of action, hence all of the stress curve charts for his various rods show a very similar profile. To the left is an example of a Garrison 209. 
One of the variables that is used in computing a stress curve is the 'length of line cast' or simply casting distance. By adding a Z axis to the standard stress curve chart, which takes into account various distances of line cast, one can see when a spot on a rod will become under- or overloaded. To the right is an example of the Dickerson 8013 from above with the addition of the line cast from 2' to 50'.