Is jumping the result of normal force or action-reaction? Just a clarification question based on an example I read about. 

Can normal force do work on an object?

The answer is yes, with an example being a person jumping. The normal force causes work to be done.
However, I'm wondering, is that actually normal force, or is that the reaction force from applying force to the ground? There is a difference between the reaction force and normal force. I'm not sure if technically that example is correct. If it isn't, can someone provide a different one where normal force does do work?
 A: 
** I'm wondering, is that actually normal force, or is that the reaction force from applying force to the ground?** There is a difference between the reaction force and normal force.

No, there is not a difference you can determine between "the reaction force" and this normal force because one is describing a relationship (reaction) and the other a reality (normal force).
It seems to me there is a fundamental misunderstanding of Newton's 3rd Law, aka, action-reaction forces. The normal force on the persons feet is caused by the interaction of the structural boundaries (the intermolecular bonds, etc) of the feet with the structural boundaries of the ground.  Likewise, the normal force on the ground from the feet is caused by exactly the same interaction. You cannot say that one occurs in "reaction" to the other.
What Newton's 3rd Law says is that forces do not occur singularly. They are interactions, and as such, if you observed the result of a force or you conceptually determine there is one force on an object, there must, by symmetry, be another force due to the same interaction. It's not a cause and effect relationship (" which force is the reaction to the action?"), it's a there-must-be-another-force-somewhere relationship. Newton's 3rd law really is a statement about conservation of momentum. This is from Newton (translated from the Latin by Drake, I believe):

If a body impinges upon another, and by its force changes the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. Teh changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, as the motions are euqally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies.

In this writing, Newton's motion is our momentum and his body is our concept of mass.
Nowhere does Newton say that an action causes a reaction. He says that forces come in pairs: 

If you press a stone with your finger, the finger is also pressed by the stone.

The forces come from a mutual interaction; reaction is an unfortunate word.
Forces have root causes and those causes are not other forces. They are interactions: mass with mass, charge with charge, quarks with quarks.
A: I would see the normal forces as a requirement to fulfil a constraint: staying on the surface of the earth. By defenition, no work is performed by constraint (reaction, normal) forces due to action-reaction.
It could be easier to look at a spring 'jumping' off a rigid table. First you compress it with your finger, which stores energy in the spring. The constraint forces make sure the spring does not enter the table, so there is no movement and therefore no work performed. When you release the spring, it will accelerate by pushing onto the table (the other end is free, so it moves). Due to inertia the spring will take off.
Now replace spring by muscles and body, and table by earth.
