Why do photons excite electrons? I know that when electrons encounter photons, they become excited and move to an orbit farther away from the nucleus of an atom as a result.  What I want to know is exactly why the photons cause the electrons to enter this state.
Edit: Sorry, I wasn't being very clear.  What I mean is, why do photons interact with electrons?
 A: Photons are electromagnetic waves that propagate in wave packet.
Those wave packet carry a defined quantized amount of energy. 
When a photon interact with an electron it will give away its energy to the electron. The electron will have more energy and hence a larger velocity. This mean that the electron will indeed "orbital" further away from the nucleus (the probability density of finding the electron will be higher further away from the nucleus).
If the new orbital of the electron is an allowed one, the electron might stay on this orbital for a while and then decay back to its ground state position. At that point the electron will emit a photon to give away the extra energy. 
If the new orbital of the electron is not an allowed one (Quantum mechanic tells you which orbital is allowed) we then say that the electron goes into a virtual states (a state that does not exist) and immediately re-emit the photon. 
You can find a mathematically more involved description here: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/photel.html
A: 
Sorry, I wasn't being very clear. What I mean is, why do photons interact with electrons?

What we have discovered up to now with our studies in physics is that there exist 4 fundamental interactions of elementary particles.
Both the photon and the electron are elementary particles and interact with the electromagnetic interaction.
Now the electrons can be free , as for example in an accelerator beam, or bound with the electromagnetic interaction in an atom, as in the hydrogen atom. 
If they are free, a photon hitting them will scatter elastically, or might give up part of its energy to the electron and go away with a smaller energy/frequency ($E=h\nu$).
If bound, it is in an energy level about the nucleus which has a unique, quantized energy, $E_1$. Over it will be unoccupied energy levels . An incoming photon, if it has an energy that corresponds to the difference between an empty  energy level $E_2$, i.e. it has energy $E_2-E_1$ can transfer its energy to the electron kicking it up and disappearing as an individual photon . The electron will probably decay from that energy level emitting a photon of energy $E_2-E_1$ but it will be a different photon. In nuclei with large $Z$ there may be cascades of photons if the energy of the initializing photon is large and there exist intermediate energy levels.
Now if we go to second quantization, the photon interacts with the electron because it is the carrier of the electromagnetic force. This covers both the bound and the unbound state of the electron, except that in the bound case still the energy has to be $E_2-E_1$ to give a large enough probability of interaction.
A: Quantum scientists came to the realization that they had to forget about the why question.  Did you notice that the answers above only talk about what happens, but not about the mechanism by which it happens?  There are some calculations that one can do about the energy of photons causing electrons to move off at a particular angle, and the energy of the photon that is left over, and the probability of such an interaction happening, but there isn't a why answer to this question in quantum mechanics.  It's just what happens. 
We can wave our hands at the phenomenon and say that since photons have wave characteristics, and since these waves are at least partly electromagnetic in character, then there is an electromagnetic field available with a photon that could push/pull an electron around. Maybe that's the best we can do for this question.
A: If the electrons orbit was like a twisted rubber band, and a photon was like a rubber band... and.. When the photon struck the bands merged to produce a bigger rubber band.... ok... and the band could be folded/twisted to match another orbital/energy level.  Then the electron is "excited" and not in the ground state.
Unfortunately that extra rubber band it absorbed cannot and won't remain permanent.  A similar amount to what was absorbed snaps back out.  Essentially a new photon is emitted.  That is how I picture it in my head.  2 s is a round rubber band ring.  2 p is a figure of 8 rubber band.  I always imagine rubber bands or ribbons because the electron can follow very exotic paths in 3 dimensions and not crash into each other :-)
Why it happens..... I don't know.  Like blobs of liquid maybe they can coalesce, but maybe the momentum of the initial photon sort of rips the coalecsed blob apart.  
Toric blobs of liquid/energy twisted into bizarre orbital shapes.  Probability functions of where a photon and electron might be and how they overlap for a short period.
A: https://www.youtube.com/watch?v=GBlE8Pc-Os4
Take a look at this video, if a photon is an oscillating electric and magnetic field then, at the right energy there is the potential to do work on an electron in one of these peaks, aka, interact with it. I hope this simple answer is what you were looking for. 
