Source of energy for magnetic work? I set two magnets on my desk such that they are experiencing attraction to each other, but due to friction with the desk, are just outside of the distance where they would snap to each other. Then I expend a small amount of work to move them closer to each other, and they snap to each other. It would appear to me that the amount of work required for this motion was greater than the amount of work I did to move them closer to each other. As a result, I am guessing something not infinitely repeatable has changed about the magnets to produce energy. What has changed?
 A: 
Magnetic attraction (and repulsion) force tails off quite quickly with distance, as anyone who has manipulated magnets will know from experience. For instance, for two point-like magnetic poles the attractive force $F \propto \frac{1}{x^2}$ with $x$ the distance between the poles. So when you double the distance then the force is reduced by a factor $4$. For real magnets the relationship is more complicated but the rule of thumb holds: higher distance reduces the force.
In the diagram above are two identical magnets, exerting an attractive magnetic force $F$ on each other. The magnets also experience a friction force $F_f=\mu mg$ (in a simple model with $\mu$ the coefficient of friction). As long as friction overcomes the magnetic force, neither magnet will move.
But you moved both magnets closer together, thereby increasing $F$ and without affecting $F_f$. If at that point $F>F_f$ then the magnets will start moving together. For one magnet the equation of motion becomes:
$ma= F-F_f$ or $a=\frac{F-F_f}{m}$, and with $F>F_f \Rightarrow a>0$. Acceleration means movement.
A: If it were two wires on your desk with steady currents between them then before hand there was a strong magnetic field, for instance between the two wires the fields from each added together to make a stronger field.
And magnetic fields have energy, really and truly. If you want to create a strong magnetic field you will have to do work. And if a strong magnetic field is destroyed then energy will be released. So when you have the wires on the table, that energy will be converted into kinetic energy (if you want to know the details about how, it sets up a Hall voltage from the charge imbalance made by the deflection of the moving charges in the magnetic field and then the corresponding work done by the electric field makes the wires themselves move as the magnetic field changes).
For permanent magnets, the picture for classical electrodynamics is more complicated. You need to either bring up magnetization of matter and a Gilbert or Ampere model of a magnetic dipole (a  choice of model for something, a fundamental magnetic dipole, that is truly a quantum mechanical thing) and then work it out from there. If you use the Ampere model it isn't so totally different than the example with the wire. The magnetic field between the magnets stored energy and as the magnets come together the field gets weaker and thus there is energy available. And eventually the energy that used to be in the magnetic field is converted into kinetic energy.
To be clear you can ignore the quantum effects by replacing the fundamental quantum magnetic dipole with an imaginary little super tiny loop of current (the Ampere model) that just has a given magnetic dipole moment. To describe the details of bow the permanent magnet works using classical electrodynamics you'd have to have regions where each little dipole points one way and regions where it points another way. You can describe the average of lots of dipole in a volume by an average dipole moment per unit volume and that is what we call magnetisation. It is fairly involved, but it is required to explain for instance how a a single called permanent magnet can gain or lose its magnetization. If you have it, they you can just have it. And if it isn't going to change for you, you can ignore how it changes. 
But there is still a magnetic field. It still has energy and when the magnets move because of the forces on the magnets that field decreases and thus stores less energy and that's where the energy comes from and the energy goes to the kinetic energy of the magnets. But it does not do so directly, which is why you sometimes hear people say "magnetic fields do no work."
They can do work on fundamental dipoles, but you either have to use a Gilbert model and have an additional force law. Or else you need to use an Ampere model and then the magnetic forces cause an interaction with the Ampere model to cause electric fields that do the work. In advanced classes you can introduce a Lagrangian or a Hamiltonian that directly has the force of a fundamental magnetic dipole and an magnetic field. In that case it turns out the force is proportional to $\vec \nabla \left(\vec \mu \cdot \vec B\right),$ so the force depends on how the magnetic field changes, not on the magnetic field itself.

that gets to what I am trying to understand. What is happening that recovers energy?

I think this is a separate question a out how the energy is recovered (you asked where it comes from), and I think that question might already have an answer (with more details) elsewhere on this site.
Weakening magnetic fields are accompanied with circulating electric fields. In empty space you can literally slosh the energy around where it can flow from one place to another, but it does require that there be both fields. This is why you can have electrostatics or magnetostatics as subjects but electrodynamics as a subject always means you study dynamic electric and magnetic fields.
It is the electric fields that ultimately delivers kinetic energy to charges (with an Ampere model of magnetic dipoles). So the current develops a charge imbalance from the magnetic field. The produces electric fields which give kinetic energy, but the changing charges and current decrease the energy stored in the magnetic field too. Technically the energy flows so each place where there are fields flows some energy to a nearby place and the place with the current and the electric field instead of giving on to its nearby regions gives some energy to the charges.
