It is transparent for several reasons. It does not absorb much light in the visible spectrum. It reflects very little light because its index of refraction is fairly close to that of air. It does not scatter light because it is usually made to be smooth compared to the wavelength of visible light.
Light, as photons, have few choices as to what can happen when they hit "stuff." Reflection, absorption, and transmission are the general classifications of options.
Since glass is not metallic, and has few "free" electrons, only about 4% of the photons will be reflected. (This is assuming the light is not all the same color. Things get more interesting with momochromatic light.)
Photons that are not reflected will interact with the atoms and molecules of the matter. If the atoms and molecules of the "stuff" have electron shells with energy differences that match the energy of the photon, then that photon will be absorbed, and it's energy will serve to heat up the material (again, this is generally speaking.)
If the atoms and moleculaes do not have such "energy transitions" that match the energy of the photon, then the photon will be absorbed and then reemitted by the atoms/molecules.
Glass so happens to not have energy transitions that match the energy of visible photons, so photons are absorbed then reemitted by each of the atoms it hits.
Glass does, however, absorb UV photons, which is why you can't get a suntan through glass.