Why does the speed of light change when is passes through different media?

Light is a wave and all waves work on the same basic principles, so let's talk about waves in general before we talk about light.  The way a wave propogates is by a disturbance in the medium occuring at one location.  Then, because the medium at that location is connected to the medium immediately adjacent to it, the medium at that start location pulls on the adjacent location, disturbing it.  Then the adjacent location pulls on the medium adjacent to it.  And it propogates out from there, always with the medium that is disturbed pulling on the adjacent medium to disturb it.  So how fast does the wave travel?  Well, it depends on how strong the force is that connects the medium to the adjacent medium.  The stronger that connection, the faster the response and the faster the wave.  The other issue that effects wave speed is how "massive" each bit of the material is.  The more massive, the more force it takes to move the medium, so the slower the wave propogates.

So let's look at a specific example.  Imagine a guitar string.  If you pluck it, a wave will propogate down the string.  The wave propogates because each section of string is attached to neighboring string and it can be stretched a very small amount.  To make that wave propogate faster, you can increase the tension on the string, which increases the force each section of string exerts on the neighboring section.  You can also make the string lighter to increase the speed (which is why high frequency strings are thinner than low frequency strings).

Now light is just an electromagnetic wave.  Instead of propogating through a material like a string, it propogates through space.  For now, just consider light in a vacuum.  A time-varying disturbance in the electric field at one location will cause an electric disturbance at the adjacent locations.  The speed of light is dictated by how quickly the adjacent space reacts to that electric field (which is measured as the magnetic permeability and electric permitivity).  But now imagine you throw in a bunch of atoms into this vaccuum (they can be in a solid, like glass, or a liquid or gas, it makes no difference).  Atoms are collections of charged particles.  They also respond to the changing electric field, since charged particles move in electric fields.  Now, not only does the electric field disturbance have to change the electric field in the adjacent location, but now it also has to push around the charges in the atom at that adjacent site.  That is basically like adding more mass to the guitar string.  So the wave will travel slower because you have effectively increased the mass of the medium.  But it is not quite that simple because the atoms can also push and pull on other atoms, so they can increase (or decrease) the force between adjacent lcoations.  That means that the speed of the electromagnetic wave will be a complicated function of how much the atom weighs, how mobile the atoms and electrons within the atom are, how much the atoms interact between eachother, and how much the atoms interact with the electric field.  Since there are so many different variables involved, you expect the speed to vary considerably based on exactly what medium the light is passing through.  The only thing you can say is that by adding atoms to a vacuum, you have to slow light down, but it is hard to know by how much without measuring it or knowing the electric permitivity and magnetic permeability of the atomic medium you are using.