Magic in Equestria is a very interesting and strange concept. Unicorns can use it extensively, and it affects Pegasi and Earth Ponies in their daily tasks. It is also present in creatures and all throughout Equestria, which leads me to wonder, what is it?
Alright, its going to get real complex past this point, so apologies.
Ok .Energy in this context I would say is the ability for something to do work. Heat energy is simply the energy of vibrating particles, kinetic is movement, doing work, chemical and nuclear are stored forms of heat and light, which both excite particles into moving, and thus doing work. Simple enough.
Why I would say Magic is a form of energy is is what it does. It primarily does work too. In terms of Pegasi, it appears to provide some form of ease in flight. This work done against the gravity of the planet means that work is being done to counteract the force. For Earth Ponies, it appears to supplement their biological strength. For unicorns, the skills we see so far are primarily levitation and teleportation, which is all about the movement of matter, once again fitting this definition of energy. In addition to this, it seems to be used in some machines too.

How this energy is generated appears to be inbred into every single pony from birth. It is an essence that appears to be only with ponies and nothing else. Now, the energy theory cannot explain the varying traits and the fact that it doesnt just float around in the air and can be refined and extracted. Thus, I have a theory that would be a little insane.

Its a cell, coded with a special particle that provides this magical energy, which is then manipulated by the cell to create differing effects. I would think this particle would be sort of like the Higgs-Boson. The particle istelf is nothing of remark, but the field surrounding it provides matter with mass. Similarly for this "Magic" particle would be generating a "magic" field around it. This could then be manipulated by the cell to provide differing effects, and the manner in which this manipulation occurs could be coded into the pony gene pool as the different races.

How this cell and associated particle would work, I have a theory. This particle is everywhere in Equestria, just like the Higgs Boson is in our world. However, this cell in the equine system is able to concentrate and manipulate these particles and their associated fields. It could potentially resonate these fields to create a sort of magic wave, similar to an Electromagnetic wave from the EM spectrum. At particular wavelengths of these fields, it can interact with other particles, and be transmitted through the air or whatever medium it encounters. These can then be concentrated on particular particles for certain effects.

Thus, using this, ponies can interact with their environment in ways they cannot see. For Pegasi for example, they could be inducing a high frequency magic wave, which could then interact with the air particles. The heating due to the induced energy could potentially either create air drafts, or mechanically push them upwards by the expanding air. For Earth Ponies, their interaction could be biological. Their cells could be inducing waves as a more powerful form of metabolism, where energy is transmitted directly to the particles in their muscles, which then can be converted back and used in some ADP-ATP reaction catalysed by this magical energy.

Then...the unicorns. Its still fits under this theory, even though its more complex.
They are able to levitate objects. Something that does not have these specialist cells. There is one possibility. Induction. Just like Electromagnetic Induction, this makes it possible that the energy is induced in the object, creating this same levitating ability of pegasi without having these particular cells. Thus, it would make the unicorn horn...essentially an antenna for this energy. A site of Magic field induction.
Transmutation is a little more difficult, but still explainable. It could be a complex form of atom smashing. Basically, its the forcing of two particular atoms together to form a new one, using the attached Magic sub-particle. By inducing it to collide at high speeds, fusion essentially takes place on a quantum scale. The heat blasts from failed magic is easily explained in this theory. Simply, unordered directional induction of this energy would simply heat the particles.
Then....teleportation. Hardest to explain or understand. The pony has to move itself to another place, with all its neurons intact. One possibility is acclerated movement at near light speed to the direction. Just using the particles around it as a heat shield, the pony moves in a vaccum state from one place to another at extreme speeds, and makes that signature blast of magic when they disappear and appear again. Why you dont see them in transit is due to the concept of light speed. When you get closer to light speed, time warps to prevent you from ever breaking the speed limit. Thus, this can magnify the apparent speed of the unicorn in question, making the shift almost instant in your perspective.

Now, I know these theories bank on there being a huge source of energy to use, since all these actions need impossibly large amounts of energy to work even on a single pony. But then again, our universe is filled with dark energy, that we havent learned to tap into....Maybe they have.