There is a lot of nonsense around about this. It is NOT a very thick stiff or cold liquid, nor is it due to how ordered the structure is. In simple terms it is all about the electrons in the substance. When photon of light enters a substance, it will interact with an electron changing its energy state.
KEY POINT — Electrons can only exist in fixed (banded) energy levels.
In common opaque material, it takes a small amount of energy to move the electron from its resting energy state to a higher energy state, so the low energy photon of visible light is absorbed, transferring its energy to the electron which in turn moves to a slightly higher energy state.
In much rarer transparent material the distance between the electrons rest energy level and the next higher state is much much greater. So because the electron can only be "resting" or at a high energy level NEVER in between, the little photon of visible light doesn't carry enough energy to transfer to the electron to make it jump to the higher state. So it keeps its power, doesn't get absorbed and passes through the material. Hey presto, see through.
Some glass only lets through light of a certain colour. This is because different colour light haas different energy levels and so depending on the energy needed to 'move' electrons to a higher energy state some colours will be strong enough and absorbed and others wont and will pass through
NOTE, I am simplifying a bit, for example it doesn't literally 'pass through' as such, the the way the electron and photon interact are quantum mechanical and none of this includes polarization, reflection etc. all of which works on a quantum level. That said on a macro scale, without the quantum detail (which would take years to teach) this is what is happening.